Pub Date : 2024-11-05DOI: 10.1016/j.csda.2024.108092
J. Álvarez-Liébana , A. López-Pérez , W. González-Manteiga , M. Febrero-Bande
High-frequency financial data can be collected as a sequence of time-ordered curves, such as intraday prices. The Functional Data Analysis (FDA) framework offers a powerful approach to uncover information embedded in the shape of the daily paths, often unavailable from classical statistical methods. A novel goodness-of-fit test for autoregressive Hilbertian (ARH) models is introduced, imposing only the Hilbert-Schmidt condition on the autocorrelation operator. The test statistic is formulated in terms of a Cramér–von Mises norm, with calibration achieved via a wild bootstrap resampling procedure. A simulation study examines the test's finite-sample performance in terms of power and size. Furthermore, a new specification test for diffusion models, including Ornstein-Uhlenbeck processes, is proposed, illustrated with an application to intraday currency exchange rates. Specifically, a two-stage methodology is proffered: firstly, the relationship between functional samples and their lagged values is assessed using an ARH(1) model; second, under linearity, a functional F-test is conducted.
高频金融数据可以作为一连串有时间顺序的曲线来收集，例如盘中价格。函数数据分析（FDA）框架提供了一种强大的方法，可以揭示蕴含在每日路径形状中的信息，而这些信息往往是经典统计方法无法获得的。本文引入了一种新的自回归希尔伯特（ARH）模型拟合优度检验，只对自相关算子施加希尔伯特-施密特条件。检验统计量是用 Cramér-von Mises 准则表示的，校准是通过野生引导重采样程序实现的。一项模拟研究考察了该检验在功率和规模方面的有限样本性能。此外，还针对扩散模型（包括奥恩斯坦-乌伦贝克过程）提出了一种新的规范检验方法，并将其应用于日内货币汇率。具体而言，提出了一种两阶段方法：首先，使用 ARH(1) 模型评估函数样本与其滞后值之间的关系；其次，在线性条件下进行函数 F 检验。
{"title":"A goodness-of-fit test for functional time series with applications to Ornstein-Uhlenbeck processes","authors":"J. Álvarez-Liébana , A. López-Pérez , W. González-Manteiga , M. Febrero-Bande","doi":"10.1016/j.csda.2024.108092","DOIUrl":"10.1016/j.csda.2024.108092","url":null,"abstract":"<div><div>High-frequency financial data can be collected as a sequence of time-ordered curves, such as intraday prices. The Functional Data Analysis (FDA) framework offers a powerful approach to uncover information embedded in the shape of the daily paths, often unavailable from classical statistical methods. A novel goodness-of-fit test for autoregressive Hilbertian (ARH) models is introduced, imposing only the Hilbert-Schmidt condition on the autocorrelation operator. The test statistic is formulated in terms of a Cramér–von Mises norm, with calibration achieved via a wild bootstrap resampling procedure. A simulation study examines the test's finite-sample performance in terms of power and size. Furthermore, a new specification test for diffusion models, including Ornstein-Uhlenbeck processes, is proposed, illustrated with an application to intraday currency exchange rates. Specifically, a two-stage methodology is proffered: firstly, the relationship between functional samples and their lagged values is assessed using an ARH(1) model; second, under linearity, a functional F-test is conducted.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"203 ","pages":"Article 108092"},"PeriodicalIF":1.5,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-04DOI: 10.1016/j.csda.2024.108078
Jongmin Mun , Sungwan Bang , Jaeoh Kim
Based on an asymptotically optimal weighted support vector machine (SVM) that introduces label shift, a systematic procedure is derived for applying oversampling and weighted SVM to extremely imbalanced datasets with a cluster-structured positive class. This method formalizes three intuitions: (i) oversampling should reflect the structure of the positive class; (ii) weights should account for both the imbalance and oversampling ratios; (iii) synthetic samples should carry less weight than the original samples. The proposed method generates synthetic samples from the estimated positive class distribution using a Gaussian mixture model. To prevent overfitting to excessive synthetic samples, different misclassification penalties are assigned to the original positive class, synthetic positive class, and negative class. The proposed method is numerically validated through simulations and an analysis of Republic of Korea Army artillery training data.
{"title":"Weighted support vector machine for extremely imbalanced data","authors":"Jongmin Mun , Sungwan Bang , Jaeoh Kim","doi":"10.1016/j.csda.2024.108078","DOIUrl":"10.1016/j.csda.2024.108078","url":null,"abstract":"<div><div>Based on an asymptotically optimal weighted support vector machine (SVM) that introduces label shift, a systematic procedure is derived for applying oversampling and weighted SVM to extremely imbalanced datasets with a cluster-structured positive class. This method formalizes three intuitions: (i) oversampling should reflect the structure of the positive class; (ii) weights should account for both the imbalance and oversampling ratios; (iii) synthetic samples should carry less weight than the original samples. The proposed method generates synthetic samples from the estimated positive class distribution using a Gaussian mixture model. To prevent overfitting to excessive synthetic samples, different misclassification penalties are assigned to the original positive class, synthetic positive class, and negative class. The proposed method is numerically validated through simulations and an analysis of Republic of Korea Army artillery training data.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"203 ","pages":"Article 108078"},"PeriodicalIF":1.5,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-04DOI: 10.1016/j.csda.2024.108090
Pao-sheng Shen
Interval sampling is an efficient sampling scheme used in epidemiological studies. Doubly truncated (DT) data arise under this sampling scheme when the failure time can be observed exactly. In practice, the failure time may not be observed and might be recorded only within time intervals, leading to doubly truncated and interval censored (DTIC) data. This article considers regression analysis of DTIC data under the Cox proportional hazards (PH) model and develops the conditional maximum likelihood estimators (cMLEs) for the regression parameters and baseline cumulative hazard function of models. The cMLEs are shown to be consistent and asymptotically normal. Simulation results indicate that the cMLEs perform well for samples of moderate size.
{"title":"Cox regression model with doubly truncated and interval-censored data","authors":"Pao-sheng Shen","doi":"10.1016/j.csda.2024.108090","DOIUrl":"10.1016/j.csda.2024.108090","url":null,"abstract":"<div><div>Interval sampling is an efficient sampling scheme used in epidemiological studies. Doubly truncated (DT) data arise under this sampling scheme when the failure time can be observed exactly. In practice, the failure time may not be observed and might be recorded only within time intervals, leading to doubly truncated and interval censored (DTIC) data. This article considers regression analysis of DTIC data under the Cox proportional hazards (PH) model and develops the conditional maximum likelihood estimators (cMLEs) for the regression parameters and baseline cumulative hazard function of models. The cMLEs are shown to be consistent and asymptotically normal. Simulation results indicate that the cMLEs perform well for samples of moderate size.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"203 ","pages":"Article 108090"},"PeriodicalIF":1.5,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fitting multivariate probit models via maximum likelihood presents considerable computational challenges, particularly in terms of computation time and convergence difficulties, even for small numbers of responses. These issues are exacerbated when dealing with ordinal data. An efficient computational approach is introduced, based on a pairwise fitting technique within a pseudo-likelihood framework. This methodology is applied to clinical case studies, specifically using a trivariate probit model. Additionally, the correlation structure among outcomes is allowed to depend on covariates, enhancing both the flexibility and interpretability of the model. By way of simulation and real data applications, the proposed approach demonstrates superior computational efficiency as the dimension of the outcome vector increases. The method's ability to capture covariate-dependent correlations makes it particularly useful in medical research, where understanding complex associations among health outcomes is of scientific importance.
{"title":"Accelerating computation: A pairwise fitting technique for multivariate probit models","authors":"Margaux Delporte , Geert Verbeke , Steffen Fieuws , Geert Molenberghs","doi":"10.1016/j.csda.2024.108082","DOIUrl":"10.1016/j.csda.2024.108082","url":null,"abstract":"<div><div>Fitting multivariate probit models via maximum likelihood presents considerable computational challenges, particularly in terms of computation time and convergence difficulties, even for small numbers of responses. These issues are exacerbated when dealing with ordinal data. An efficient computational approach is introduced, based on a pairwise fitting technique within a pseudo-likelihood framework. This methodology is applied to clinical case studies, specifically using a trivariate probit model. Additionally, the correlation structure among outcomes is allowed to depend on covariates, enhancing both the flexibility and interpretability of the model. By way of simulation and real data applications, the proposed approach demonstrates superior computational efficiency as the dimension of the outcome vector increases. The method's ability to capture covariate-dependent correlations makes it particularly useful in medical research, where understanding complex associations among health outcomes is of scientific importance.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"203 ","pages":"Article 108082"},"PeriodicalIF":1.5,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The parallel algorithm is widely recognized for its effectiveness in handling large-scale datasets stored in a distributed manner, making it a popular choice for solving statistical learning models. However, there is currently limited research on parallel algorithms specifically designed for high-dimensional regression with combined regularization terms. These terms, such as elastic-net, sparse group lasso, sparse fused lasso, and their nonconvex variants, have gained significant attention in various fields due to their ability to incorporate prior information and promote sparsity within specific groups or fused variables. The scarcity of parallel algorithms for combined regularizations can be attributed to the inherent nonsmoothness and complexity of these terms, as well as the absence of closed-form solutions for certain proximal operators associated with them. This paper proposes a unified constrained optimization formulation based on the consensus problem for these types of convex and nonconvex regression problems, and derives the corresponding parallel alternating direction method of multipliers (ADMM) algorithms. Furthermore, it is proven that the proposed algorithm not only has global convergence but also exhibits a linear convergence rate. It is worth noting that the computational complexity of the proposed algorithm remains the same for different regularization terms and losses, which implicitly demonstrates the universality of this algorithm. Extensive simulation experiments, along with a financial example, serve to demonstrate the reliability, stability, and scalability of our algorithm. The R package for implementing the proposed algorithm can be obtained at https://github.com/xfwu1016/CPADMM.
并行算法在处理以分布式方式存储的大规模数据集方面的有效性已得到广泛认可，因此成为解决统计学习模型的热门选择。然而，目前专门针对具有组合正则化条款的高维回归而设计的并行算法的研究还很有限。这些术语，如 elastic-net、sparse group lasso、sparse fused lasso 及其非凸变体，由于能够在特定组或融合变量内纳入先验信息并促进稀疏性，在各个领域都获得了极大的关注。组合正则化并行算法的匮乏可归因于这些术语固有的非平稳性和复杂性，以及与之相关的某些近似算子缺乏闭式解。本文针对这些类型的凸回归和非凸回归问题，提出了基于共识问题的统一约束优化公式，并推导出相应的并行交替乘法（ADMM）算法。此外，还证明了所提出的算法不仅具有全局收敛性，而且还表现出线性收敛率。值得注意的是，对于不同的正则化项和损失，所提算法的计算复杂度保持不变，这隐含地证明了该算法的通用性。大量的模拟实验以及一个财务实例证明了我们算法的可靠性、稳定性和可扩展性。实现该算法的 R 软件包可从 https://github.com/xfwu1016/CPADMM 获取。
{"title":"A unified consensus-based parallel algorithm for high-dimensional regression with combined regularizations","authors":"Xiaofei Wu , Rongmei Liang , Zhimin Zhang , Zhenyu Cui","doi":"10.1016/j.csda.2024.108081","DOIUrl":"10.1016/j.csda.2024.108081","url":null,"abstract":"<div><div>The parallel algorithm is widely recognized for its effectiveness in handling large-scale datasets stored in a distributed manner, making it a popular choice for solving statistical learning models. However, there is currently limited research on parallel algorithms specifically designed for high-dimensional regression with combined regularization terms. These terms, such as elastic-net, sparse group lasso, sparse fused lasso, and their nonconvex variants, have gained significant attention in various fields due to their ability to incorporate prior information and promote sparsity within specific groups or fused variables. The scarcity of parallel algorithms for combined regularizations can be attributed to the inherent nonsmoothness and complexity of these terms, as well as the absence of closed-form solutions for certain proximal operators associated with them. This paper proposes a <em>unified</em> constrained optimization formulation based on the consensus problem for these types of convex and nonconvex regression problems, and derives the corresponding parallel alternating direction method of multipliers (ADMM) algorithms. Furthermore, it is proven that the proposed algorithm not only has global convergence but also exhibits a linear convergence rate. It is worth noting that the computational complexity of the proposed algorithm remains the same for different regularization terms and losses, which implicitly demonstrates the universality of this algorithm. Extensive simulation experiments, along with a financial example, serve to demonstrate the reliability, stability, and scalability of our algorithm. The R package for implementing the proposed algorithm can be obtained at <span><span>https://github.com/xfwu1016/CPADMM</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"203 ","pages":"Article 108081"},"PeriodicalIF":1.5,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-29DOI: 10.1016/j.csda.2024.108073
Anthony-Alexander Christidis , Stefan Van Aelst , Ruben Zamar
The two primary approaches for high-dimensional regression problems are sparse methods (e.g., best subset selection, which uses the -norm in the penalty) and ensemble methods (e.g., random forests). Although sparse methods typically yield interpretable models, in terms of prediction accuracy they are often outperformed by “blackbox” multi-model ensemble methods. A regression ensemble is introduced which combines the interpretability of sparse methods with the high prediction accuracy of ensemble methods. An algorithm is proposed to solve the joint optimization of the corresponding -penalized regression models by extending recent developments in -optimization for sparse methods to multi-model regression ensembles. The sparse and diverse models in the ensemble are learned simultaneously from the data. Each of these models provides an explanation for the relationship between a subset of predictors and the response variable. Empirical studies and theoretical knowledge about ensembles are used to gain insight into the ensemble method's performance, focusing on the interplay between bias, variance, covariance, and variable selection. In prediction tasks, the ensembles can outperform state-of-the-art competitors on both simulated and real data. Forward stepwise regression is also generalized to multi-model regression ensembles and used to obtain an initial solution for the algorithm. The optimization algorithms are implemented in publicly available software packages.
{"title":"Multi-model subset selection","authors":"Anthony-Alexander Christidis , Stefan Van Aelst , Ruben Zamar","doi":"10.1016/j.csda.2024.108073","DOIUrl":"10.1016/j.csda.2024.108073","url":null,"abstract":"<div><div>The two primary approaches for high-dimensional regression problems are sparse methods (e.g., best subset selection, which uses the <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-norm in the penalty) and ensemble methods (e.g., random forests). Although sparse methods typically yield interpretable models, in terms of prediction accuracy they are often outperformed by “blackbox” multi-model ensemble methods. A regression ensemble is introduced which combines the interpretability of sparse methods with the high prediction accuracy of ensemble methods. An algorithm is proposed to solve the joint optimization of the corresponding <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-penalized regression models by extending recent developments in <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-optimization for sparse methods to multi-model regression ensembles. The sparse and diverse models in the ensemble are learned simultaneously from the data. Each of these models provides an explanation for the relationship between a subset of predictors and the response variable. Empirical studies and theoretical knowledge about ensembles are used to gain insight into the ensemble method's performance, focusing on the interplay between bias, variance, covariance, and variable selection. In prediction tasks, the ensembles can outperform state-of-the-art competitors on both simulated and real data. Forward stepwise regression is also generalized to multi-model regression ensembles and used to obtain an initial solution for the algorithm. The optimization algorithms are implemented in publicly available software packages.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"203 ","pages":"Article 108073"},"PeriodicalIF":1.5,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-26DOI: 10.1016/j.csda.2024.108076
Claudia Czado
Gaussian linear structural equation models (SEMs) are often used as a statistical model associated with a directed acyclic graph (DAG) also known as a Bayesian network. However, such a model might not be able to represent the non-Gaussian dependence present in some data sets resulting in nonlinear, non-additive and non Gaussian conditional distributions. Therefore the use of the class of D-vine copula based regression models for the specification of the conditional distribution of a node given its parents is proposed. This class extends the class of standard linear regression models considerably. The approach also allows to create an importance order of the parents of each node and gives the potential to remove edges from the starting DAG not supported by the data. Further uncertainty of conditional estimates can be assessed and fast generative simulation using the D-vine copula based SEM is available. The improvement over a Gaussian linear SEM is shown using random specifications of the D-vine based SEM as well as its ability to correctly remove edges not present in the data generation using simulation. An engineering application showcases the usefulness of the proposals.
高斯线性结构方程模型（SEM）通常被用作与有向无环图（DAG）（也称为贝叶斯网络）相关的统计模型。然而，这种模型可能无法表示某些数据集中存在的非高斯依赖性，从而导致非线性、非相加和非高斯条件分布。因此，我们建议使用基于 D-vine copula 的回归模型来指定一个节点的条件分布（给定其父节点）。这一类模型大大扩展了标准线性回归模型。该方法还允许创建每个节点父节点的重要性顺序，并有可能从起始 DAG 中删除数据不支持的边。此外，还可以评估条件估计值的不确定性，并使用基于 D-vine copula 的 SEM 进行快速生成模拟。与高斯线性 SEM 相比，基于 D-藤的 SEM 使用随机规格显示了其改进之处，并显示了其通过模拟正确移除数据生成中不存在的边的能力。一个工程应用展示了这些建议的实用性。
{"title":"Vine copula based structural equation models","authors":"Claudia Czado","doi":"10.1016/j.csda.2024.108076","DOIUrl":"10.1016/j.csda.2024.108076","url":null,"abstract":"<div><div>Gaussian linear structural equation models (SEMs) are often used as a statistical model associated with a directed acyclic graph (DAG) also known as a Bayesian network. However, such a model might not be able to represent the non-Gaussian dependence present in some data sets resulting in nonlinear, non-additive and non Gaussian conditional distributions. Therefore the use of the class of D-vine copula based regression models for the specification of the conditional distribution of a node given its parents is proposed. This class extends the class of standard linear regression models considerably. The approach also allows to create an importance order of the parents of each node and gives the potential to remove edges from the starting DAG not supported by the data. Further uncertainty of conditional estimates can be assessed and fast generative simulation using the D-vine copula based SEM is available. The improvement over a Gaussian linear SEM is shown using random specifications of the D-vine based SEM as well as its ability to correctly remove edges not present in the data generation using simulation. An engineering application showcases the usefulness of the proposals.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"203 ","pages":"Article 108076"},"PeriodicalIF":1.5,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In high-dimensional linear regression models, common assumptions typically entail sparsity of regression coefficients . However, these assumptions may not hold when the majority, if not all, of regression coefficients are non-zeros. Statistical methods designed for sparse models may lead to substantial bias in model estimation. Therefore, this article proposes a novel Bayesian Grouping-Gibbs Sampling (BGGS) method, which departs from the common sparse assumptions in high-dimensional problems. The BGGS method leverages a grouping strategy that partitions β into distinct groups, facilitating rapid sampling in high-dimensional space. The grouping number (k) can be determined using the ‘Elbow plot’, which operates efficiently and is robust against the initial value. Theoretical analysis, under some regular conditions, guarantees model selection and parameter estimation consistency, and bound for the prediction error. Furthermore, three finite simulations are conducted to assess the competitive advantages of the proposed method in terms of parameter estimation and prediction accuracy. Finally, the BGGS method is applied to a financial dataset to explore its practical utility.
{"title":"Bayesian grouping-Gibbs sampling estimation of high-dimensional linear model with non-sparsity","authors":"Shanshan Qin , Guanlin Zhang , Yuehua Wu , Zhongyi Zhu","doi":"10.1016/j.csda.2024.108072","DOIUrl":"10.1016/j.csda.2024.108072","url":null,"abstract":"<div><div>In high-dimensional linear regression models, common assumptions typically entail sparsity of regression coefficients <span><math><mi>β</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>. However, these assumptions may not hold when the majority, if not all, of regression coefficients are non-zeros. Statistical methods designed for sparse models may lead to substantial bias in model estimation. Therefore, this article proposes a novel Bayesian Grouping-Gibbs Sampling (BGGS) method, which departs from the common sparse assumptions in high-dimensional problems. The BGGS method leverages a grouping strategy that partitions <strong><em>β</em></strong> into distinct groups, facilitating rapid sampling in high-dimensional space. The grouping number (<em>k</em>) can be determined using the ‘Elbow plot’, which operates efficiently and is robust against the initial value. Theoretical analysis, under some regular conditions, guarantees model selection and parameter estimation consistency, and bound for the prediction error. Furthermore, three finite simulations are conducted to assess the competitive advantages of the proposed method in terms of parameter estimation and prediction accuracy. Finally, the BGGS method is applied to a financial dataset to explore its practical utility.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"203 ","pages":"Article 108072"},"PeriodicalIF":1.5,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-21DOI: 10.1016/j.csda.2024.108079
Shanshan Luo , Jiaqi Min , Wei Li , Xueli Wang , Zhi Geng
Propensity score based estimators are commonly employed in observational studies to address baseline confounders, without explicitly modeling their association with the outcome. In this paper, to fully leverage these estimators, we consider a series of regression models for improving estimation efficiency. The proposed estimators rely solely on a properly modeled propensity score and do not require the correct specification of outcome models. In addition, we consider a comparative analysis by applying the proposed estimators to four different adjustment sets, each consisting of background covariates. The theoretical results imply that incorporating predictive covariates into both propensity score and regression model demonstrates the lowest asymptotic variance. However, including instrumental variables in the propensity score may decrease the estimation efficiency of the proposed estimators. To evaluate the performance of the proposed estimators, we conduct simulation studies and provide a real data example.
{"title":"A comparative analysis of different adjustment sets using propensity score based estimators","authors":"Shanshan Luo , Jiaqi Min , Wei Li , Xueli Wang , Zhi Geng","doi":"10.1016/j.csda.2024.108079","DOIUrl":"10.1016/j.csda.2024.108079","url":null,"abstract":"<div><div>Propensity score based estimators are commonly employed in observational studies to address baseline confounders, without explicitly modeling their association with the outcome. In this paper, to fully leverage these estimators, we consider a series of regression models for improving estimation efficiency. The proposed estimators rely solely on a properly modeled propensity score and do not require the correct specification of outcome models. In addition, we consider a comparative analysis by applying the proposed estimators to four different adjustment sets, each consisting of background covariates. The theoretical results imply that incorporating predictive covariates into both propensity score and regression model demonstrates the lowest asymptotic variance. However, including instrumental variables in the propensity score may decrease the estimation efficiency of the proposed estimators. To evaluate the performance of the proposed estimators, we conduct simulation studies and provide a real data example.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"203 ","pages":"Article 108079"},"PeriodicalIF":1.5,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-17DOI: 10.1016/j.csda.2024.108074
Shuang Sun , Zening Song , Xiaojun Song
Based on a residual marked empirical process, Cramér–von Mises and Kolmogorov–Smirnov tests are proposed for the correct specification of the nonparametric components in partially linear time series models. The tests are unified in the sense that the asymptotic distribution of residual marked empirical process is invariant across different -consistent estimators in calculating residuals (where ) under the null. In addition, the residual marked empirical process has the same power property under the sequence of local alternatives regardless of the estimators used. Achieved through a projection method, these features also enable using a computationally convenient multiplier bootstrap to approximate the unified null distributions of the test statistics. Simulations show satisfactory finite-sample performance of the proposed method. The application to validate the parametric form of conditional variance in the ARCH-X model is also highlighted, along with an empirical analysis of the conditional variance of the FTSE 100 index return series.
{"title":"Unified specification tests in partially linear time series models","authors":"Shuang Sun , Zening Song , Xiaojun Song","doi":"10.1016/j.csda.2024.108074","DOIUrl":"10.1016/j.csda.2024.108074","url":null,"abstract":"<div><div>Based on a residual marked empirical process, Cramér–von Mises and Kolmogorov–Smirnov tests are proposed for the correct specification of the nonparametric components in partially linear time series models. The tests are unified in the sense that the asymptotic distribution of residual marked empirical process is invariant across different <span><math><msup><mrow><mi>n</mi></mrow><mrow><mi>ν</mi></mrow></msup></math></span>-consistent estimators in calculating residuals (where <span><math><mi>ν</mi><mo>></mo><mn>1</mn><mo>/</mo><mn>4</mn></math></span>) under the null. In addition, the residual marked empirical process has the same power property under the sequence of local alternatives regardless of the estimators used. Achieved through a projection method, these features also enable using a computationally convenient multiplier bootstrap to approximate the unified null distributions of the test statistics. Simulations show satisfactory finite-sample performance of the proposed method. The application to validate the parametric form of conditional variance in the ARCH-X model is also highlighted, along with an empirical analysis of the conditional variance of the FTSE 100 index return series.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"203 ","pages":"Article 108074"},"PeriodicalIF":1.5,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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