Pub Date : 2025-06-19DOI: 10.1016/j.csda.2025.108234
Qihu Zhang , Jongik Chung , Cheolwoo Park
Methods are proposed for estimating multiple precision matrices for long-memory time series, with particular emphasis on the analysis of resting-state functional magnetic resonance imaging (fMRI) data obtained from multiple subjects. The objective is to estimate both individual brain networks and a common structure representative of a group. Several approaches employing weighted aggregation are introduced to simultaneously estimate individual and group-level precision matrices. Convergence rates of the estimators are examined under various norms and expectations, and their performance is evaluated under both sub-Gaussian and heavy-tailed distributions. The proposed methods are demonstrated through simulated data and real resting-state fMRI datasets.
{"title":"Joint estimation of precision matrices for long-memory time series","authors":"Qihu Zhang , Jongik Chung , Cheolwoo Park","doi":"10.1016/j.csda.2025.108234","DOIUrl":"10.1016/j.csda.2025.108234","url":null,"abstract":"<div><div>Methods are proposed for estimating multiple precision matrices for long-memory time series, with particular emphasis on the analysis of resting-state functional magnetic resonance imaging (fMRI) data obtained from multiple subjects. The objective is to estimate both individual brain networks and a common structure representative of a group. Several approaches employing weighted aggregation are introduced to simultaneously estimate individual and group-level precision matrices. Convergence rates of the estimators are examined under various norms and expectations, and their performance is evaluated under both sub-Gaussian and heavy-tailed distributions. The proposed methods are demonstrated through simulated data and real resting-state fMRI datasets.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"212 ","pages":"Article 108234"},"PeriodicalIF":1.5,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338392","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 : 2025-06-16DOI: 10.1016/j.csda.2025.108231
Giuseppina Albano , Virginia Giorno , Gema Pérez-Romero , Francisco de Asis Torres-Ruiz
A Susceptible-Infected-Removed stochastic model is presented, in which the stochasticity is introduced through two independent Brownian motions in the dynamics of the Susceptible and Infected populations. To account for the natural evolution of the Susceptible population, a growth function is considered in which size is influenced by the birth and death of individuals. Inference for such a model is addressed by means of a Quasi Maximum Likelihood Estimation (QMLE) method. The resulting nonlinear system can be numerically solved by iterative procedures. A technique to obtain the initial solutions usually required by such methods is also provided. Finally, simulation studies are performed for three well-known growth functions, namely Gompertz, Logistic and Bertalanffy curves. The performance of the initial estimates of the involved parameters is assessed, and the goodness of the proposed methodology is evaluated.
提出了一种易感-感染-去除随机模型，该模型通过易感种群和感染种群动力学中的两个独立布朗运动引入随机性。为了解释易感群体的自然进化，考虑了一个生长函数，其中大小受个体出生和死亡的影响。利用拟极大似然估计（Quasi Maximum Likelihood Estimation， QMLE）方法解决了该模型的推理问题。所得到的非线性系统可以通过迭代过程进行数值求解。本文还提供了一种获得这些方法通常需要的初始解的技术。最后，对Gompertz曲线、Logistic曲线和Bertalanffy曲线这三种著名的生长函数进行了仿真研究。评估了所涉及参数的初始估计的性能，并评估了所提出方法的优点。
{"title":"Inference on a stochastic SIR model including growth curves","authors":"Giuseppina Albano , Virginia Giorno , Gema Pérez-Romero , Francisco de Asis Torres-Ruiz","doi":"10.1016/j.csda.2025.108231","DOIUrl":"10.1016/j.csda.2025.108231","url":null,"abstract":"<div><div>A Susceptible-Infected-Removed stochastic model is presented, in which the stochasticity is introduced through two independent Brownian motions in the dynamics of the Susceptible and Infected populations. To account for the natural evolution of the Susceptible population, a growth function is considered in which size is influenced by the birth and death of individuals. Inference for such a model is addressed by means of a Quasi Maximum Likelihood Estimation (QMLE) method. The resulting nonlinear system can be numerically solved by iterative procedures. A technique to obtain the initial solutions usually required by such methods is also provided. Finally, simulation studies are performed for three well-known growth functions, namely Gompertz, Logistic and Bertalanffy curves. The performance of the initial estimates of the involved parameters is assessed, and the goodness of the proposed methodology is evaluated.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"212 ","pages":"Article 108231"},"PeriodicalIF":1.5,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338395","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 : 2025-06-09DOI: 10.1016/j.csda.2025.108230
Shanghao Wu , Xiao Guo , Hai Zhang
Multi-layer networks arise naturally in various scientific domains including social sciences, biology, neuroscience, among others. The network layers of a given multi-layer network are commonly stored in a local and distributed fashion because of the privacy, ownership, and communication costs. The literature on community detection based on these data is still limited. This paper proposes a new distributed spectral clustering-based algorithm for consensus community detection of the locally stored multi-layer network. The algorithm is based on the power method. It is communication-efficient by allowing multiple local power iterations before aggregation; and privacy-preserving by incorporating the notion of differential privacy. The convergence rate of the proposed algorithm is studied under the assumption that the multi-layer networks are generated from the multi-layer stochastic block models. Numerical studies show the superior performance of the proposed algorithm over competitive algorithms.
{"title":"Privacy-preserving communication-efficient spectral clustering for distributed multiple networks","authors":"Shanghao Wu , Xiao Guo , Hai Zhang","doi":"10.1016/j.csda.2025.108230","DOIUrl":"10.1016/j.csda.2025.108230","url":null,"abstract":"<div><div>Multi-layer networks arise naturally in various scientific domains including social sciences, biology, neuroscience, among others. The network layers of a given multi-layer network are commonly stored in a local and distributed fashion because of the privacy, ownership, and communication costs. The literature on community detection based on these data is still limited. This paper proposes a new distributed spectral clustering-based algorithm for consensus community detection of the locally stored multi-layer network. The algorithm is based on the power method. It is communication-efficient by allowing multiple local power iterations before aggregation; and privacy-preserving by incorporating the notion of differential privacy. The convergence rate of the proposed algorithm is studied under the assumption that the multi-layer networks are generated from the multi-layer stochastic block models. Numerical studies show the superior performance of the proposed algorithm over competitive algorithms.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"212 ","pages":"Article 108230"},"PeriodicalIF":1.5,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144261609","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 : 2025-06-05DOI: 10.1016/j.csda.2025.108229
Yichen Lou , Yuqing Ma , Liming Xiang , Jianguo Sun
Interval-censored competing risks data arise in many cohort studies in clinical research, where multiple types of events subject to interval censoring are included and the occurrence of the primary event of interest may be censored by the occurrence of other events. The presence of missing event types and left truncation poses challenges to the regression analysis of such data. We propose a new two-stage estimation procedure under a class of semiparametric generalized odds rate transformation models to overcome these challenges. Our method first facilitates the estimation of both the probability of response and the probability of occurrence of each type of event under the missing at random assumption, using either parametric or non-parametric methods. An augmented inverse probability weighting likelihood based on the complete-case likelihood and data from subjects with missing type of event is then maximized for estimating regression parameters. We provide desirable asymptotic properties and construct a concordance index to evaluate the model's discriminative ability. The proposed method is demonstrated through extensive simulations and the analysis of data from the Amsterdam cohort study on HIV infection and AIDS.
{"title":"Flexible modeling of left-truncated and interval-censored competing risks data with missing event types","authors":"Yichen Lou , Yuqing Ma , Liming Xiang , Jianguo Sun","doi":"10.1016/j.csda.2025.108229","DOIUrl":"10.1016/j.csda.2025.108229","url":null,"abstract":"<div><div>Interval-censored competing risks data arise in many cohort studies in clinical research, where multiple types of events subject to interval censoring are included and the occurrence of the primary event of interest may be censored by the occurrence of other events. The presence of missing event types and left truncation poses challenges to the regression analysis of such data. We propose a new two-stage estimation procedure under a class of semiparametric generalized odds rate transformation models to overcome these challenges. Our method first facilitates the estimation of both the probability of response and the probability of occurrence of each type of event under the missing at random assumption, using either parametric or non-parametric methods. An augmented inverse probability weighting likelihood based on the complete-case likelihood and data from subjects with missing type of event is then maximized for estimating regression parameters. We provide desirable asymptotic properties and construct a concordance index to evaluate the model's discriminative ability. The proposed method is demonstrated through extensive simulations and the analysis of data from the Amsterdam cohort study on HIV infection and AIDS.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"211 ","pages":"Article 108229"},"PeriodicalIF":1.5,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242893","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 : 2025-06-03DOI: 10.1016/j.csda.2025.108226
Guang Yang , Long Feng
Image clustering is usually conducted by vectorizing image pixels, treating them as independent, and applying classical clustering approaches to the obtained features. However, as image data is often of high-dimensional and contains rich spatial information, such treatment is far from satisfactory. For medical image data, another important characteristic is the region-wise sparseness in signals. That is to say, there are only a few unknown regions in the medical image that differentiate the images associated with different groups of patients, while other regions are uninformative. Accurately detecting these informative regions would not only improve clustering accuracy, more importantly, it would also provide interpretations for the rationale behind them. Motivated by the need to identify significant regions of interest, we propose a general framework named Image Clustering via Sparse Kronecker Product Decomposition (IC-SKPD). This framework aims to simultaneously divide samples into clusters and detect regions that are informative for clustering. Our framework is general in the sense that it provides a unified treatment for matrix and tensor-valued samples. An iterative hard-thresholded singular value decomposition approach is developed to solve this model. Theoretically, the IC-SKPD enjoys guarantees for clustering accuracy and region detection consistency under mild conditions on the minimum signals. Comprehensive simulations along with real data analysis further validate the superior performance of IC-SKPD on clustering and region detection.
{"title":"Region detection and image clustering via sparse Kronecker product decomposition","authors":"Guang Yang , Long Feng","doi":"10.1016/j.csda.2025.108226","DOIUrl":"10.1016/j.csda.2025.108226","url":null,"abstract":"<div><div>Image clustering is usually conducted by vectorizing image pixels, treating them as independent, and applying classical clustering approaches to the obtained features. However, as image data is often of high-dimensional and contains rich spatial information, such treatment is far from satisfactory. For medical image data, another important characteristic is the region-wise sparseness in signals. That is to say, there are only a few unknown regions in the medical image that differentiate the images associated with different groups of patients, while other regions are uninformative. Accurately detecting these informative regions would not only improve clustering accuracy, more importantly, it would also provide interpretations for the rationale behind them. Motivated by the need to identify significant regions of interest, we propose a general framework named Image Clustering via Sparse Kronecker Product Decomposition (IC-SKPD). This framework aims to simultaneously divide samples into clusters and detect regions that are informative for clustering. Our framework is general in the sense that it provides a unified treatment for matrix and tensor-valued samples. An iterative hard-thresholded singular value decomposition approach is developed to solve this model. Theoretically, the IC-SKPD enjoys guarantees for clustering accuracy and region detection consistency under mild conditions on the minimum signals. Comprehensive simulations along with real data analysis further validate the superior performance of IC-SKPD on clustering and region detection.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"211 ","pages":"Article 108226"},"PeriodicalIF":1.5,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242892","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 : 2025-06-03DOI: 10.1016/j.csda.2025.108227
Changxin Yang , Zhongyi Zhu , Hongmei Lin , Zengyan Fan , Heng Lian
While there is a substantial body of research on high-dimensional regression with left-censored responses, few methods address this problem in a distributed manner. Due to data transmission limitations and privacy concerns, centralizing all data is often impractical, necessitating a method for collaborative learning with distributed data. In this paper, we employ the Iterative Hard Thresholding (IHT) method for the Tobit model to address this challenge, allowing one to directly specify the desired sparsity and offering an alternative estimation and variable selection approach. Theoretical analysis shows that our estimator achieves a nearly minimax-optimal convergence rate using only a few rounds of communication. Its practical performance is evaluated under both the pooled and the distributed setting. The former highlights its competitive estimation efficiency and variable selection performance compared to existing approaches, while the latter demonstrates that the decentralized estimator closely matches the performance of its centralized counterpart. When applied to high-dimensional left-censored HIV viral load data, our method also demonstrates comparable performance.
{"title":"Distributed iterative hard thresholding for variable selection in Tobit models","authors":"Changxin Yang , Zhongyi Zhu , Hongmei Lin , Zengyan Fan , Heng Lian","doi":"10.1016/j.csda.2025.108227","DOIUrl":"10.1016/j.csda.2025.108227","url":null,"abstract":"<div><div>While there is a substantial body of research on high-dimensional regression with left-censored responses, few methods address this problem in a distributed manner. Due to data transmission limitations and privacy concerns, centralizing all data is often impractical, necessitating a method for collaborative learning with distributed data. In this paper, we employ the Iterative Hard Thresholding (IHT) method for the Tobit model to address this challenge, allowing one to directly specify the desired sparsity and offering an alternative estimation and variable selection approach. Theoretical analysis shows that our estimator achieves a nearly minimax-optimal convergence rate using only a few rounds of communication. Its practical performance is evaluated under both the pooled and the distributed setting. The former highlights its competitive estimation efficiency and variable selection performance compared to existing approaches, while the latter demonstrates that the decentralized estimator closely matches the performance of its centralized counterpart. When applied to high-dimensional left-censored HIV viral load data, our method also demonstrates comparable performance.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"211 ","pages":"Article 108227"},"PeriodicalIF":1.5,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203578","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 : 2025-06-02DOI: 10.1016/j.csda.2025.108228
Alan T. Arakkal, Daniel K. Sewell
While latent space network models have been a popular approach for community detection for over 15 years, major computational challenges remain, limiting the ability to scale beyond small networks. The R statistical software package, JANE, introduces a new estimation algorithm with massive speedups derived from: (1) a low dimensional approximation approach to adjust for degree heterogeneity parameters; (2) an approximation of intractable likelihood terms; (3) a fast initialization algorithm; and (4) a novel set of convergence criteria focused on clustering performance. Additionally, the proposed method addresses limitations of current implementations, which rely on a restrictive spherical-shape assumption for the prior distribution on the latent positions; relaxing this constraint allows for greater flexibility across diverse network structures. A simulation study evaluating clustering performance of the proposed approach against state-of-the-art methods shows dramatically improved clustering performance in most scenarios and significant reductions in computational time — up to 45 times faster compared to existing approaches.
{"title":"JANE: Just Another latent space NEtwork clustering algorithm","authors":"Alan T. Arakkal, Daniel K. Sewell","doi":"10.1016/j.csda.2025.108228","DOIUrl":"10.1016/j.csda.2025.108228","url":null,"abstract":"<div><div>While latent space network models have been a popular approach for community detection for over 15 years, major computational challenges remain, limiting the ability to scale beyond small networks. The R statistical software package, <span>JANE</span>, introduces a new estimation algorithm with massive speedups derived from: (1) a low dimensional approximation approach to adjust for degree heterogeneity parameters; (2) an approximation of intractable likelihood terms; (3) a fast initialization algorithm; and (4) a novel set of convergence criteria focused on clustering performance. Additionally, the proposed method addresses limitations of current implementations, which rely on a restrictive spherical-shape assumption for the prior distribution on the latent positions; relaxing this constraint allows for greater flexibility across diverse network structures. A simulation study evaluating clustering performance of the proposed approach against state-of-the-art methods shows dramatically improved clustering performance in most scenarios and significant reductions in computational time — up to 45 times faster compared to existing approaches.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"211 ","pages":"Article 108228"},"PeriodicalIF":1.5,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222027","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 : 2025-06-02DOI: 10.1016/j.csda.2025.108219
Tom Stindl , Zelong Bi , Clara Grazian
Spatiotemporal Renewal Epidemic Type Aftershock Sequence models are self-exciting point processes that model the occurrence time, epicenter, and magnitude of earthquakes in a geographical region. The arrival rate of earthquakes is formulated as the superposition of a main shock renewal process and homogeneous Poisson processes for the aftershocks, motivated by empirical laws in seismology. Existing methods for model fitting rely on maximizing the log-likelihood by either direct numerical optimization or Expectation Maximization algorithms, both of which can suffer from convergence issues and lack adequate quantification of parameter estimation uncertainty. To address these limitations, a Bayesian approach is employed, with posterior inference carried out using a data augmentation strategy within a Markov chain Monte Carlo framework. The branching structure is treated as a latent variable to improve sampling efficiency, and a purpose-built Hamiltonian Monte Carlo sampler is implemented to update the parameters within the Gibbs sampler. This methodology enables parameter uncertainty to be incorporated into forecasts of seismicity. Estimation and forecasting are demonstrated on simulated catalogs and an earthquake catalog from Italy. R code implementing the methods is provided in the Supplementary Materials.
{"title":"Bayesian forecasting of Italian seismicity using the spatiotemporal RETAS model","authors":"Tom Stindl , Zelong Bi , Clara Grazian","doi":"10.1016/j.csda.2025.108219","DOIUrl":"10.1016/j.csda.2025.108219","url":null,"abstract":"<div><div>Spatiotemporal Renewal Epidemic Type Aftershock Sequence models are self-exciting point processes that model the occurrence time, epicenter, and magnitude of earthquakes in a geographical region. The arrival rate of earthquakes is formulated as the superposition of a main shock renewal process and homogeneous Poisson processes for the aftershocks, motivated by empirical laws in seismology. Existing methods for model fitting rely on maximizing the log-likelihood by either direct numerical optimization or Expectation Maximization algorithms, both of which can suffer from convergence issues and lack adequate quantification of parameter estimation uncertainty. To address these limitations, a Bayesian approach is employed, with posterior inference carried out using a data augmentation strategy within a Markov chain Monte Carlo framework. The branching structure is treated as a latent variable to improve sampling efficiency, and a purpose-built Hamiltonian Monte Carlo sampler is implemented to update the parameters within the Gibbs sampler. This methodology enables parameter uncertainty to be incorporated into forecasts of seismicity. Estimation and forecasting are demonstrated on simulated catalogs and an earthquake catalog from Italy. <span>R</span> code implementing the methods is provided in the Supplementary Materials.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"212 ","pages":"Article 108219"},"PeriodicalIF":1.5,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144261610","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 : 2025-05-30DOI: 10.1016/j.csda.2025.108218
Nicolas Frink, Timo Schmid
Small area estimation methods are proposed that use generalized tree-based machine learning techniques to improve the estimation of disaggregated means in small areas using discrete survey data. Specifically, two existing approaches based on random forests - the Generalized Mixed Effects Random Forest (GMERF) and a Mixed Effects Random Forest (MERF) - are extended to accommodate count outcomes, addressing key challenges such as overdispersion. Additionally, three bootstrap methodologies designed to assess the reliability of point estimators for area-level means are evaluated. The numerical analysis shows that the MERF, which does not assume a Poisson distribution to model the mean behavior of count data, excels in scenarios of severe overdispersion. Conversely, the GMERF performs best under conditions where Poisson distribution assumptions are moderately met. In a case study using real-world data from the state of Guerrero, Mexico, the proposed methods effectively estimate area-level means while capturing the uncertainty inherent in overdispersed count data. These findings highlight their practical applicability for small area estimation.
{"title":"Small area prediction of counts under machine learning-type mixed models","authors":"Nicolas Frink, Timo Schmid","doi":"10.1016/j.csda.2025.108218","DOIUrl":"10.1016/j.csda.2025.108218","url":null,"abstract":"<div><div>Small area estimation methods are proposed that use generalized tree-based machine learning techniques to improve the estimation of disaggregated means in small areas using discrete survey data. Specifically, two existing approaches based on random forests - the Generalized Mixed Effects Random Forest (GMERF) and a Mixed Effects Random Forest (MERF) - are extended to accommodate count outcomes, addressing key challenges such as overdispersion. Additionally, three bootstrap methodologies designed to assess the reliability of point estimators for area-level means are evaluated. The numerical analysis shows that the MERF, which does not assume a Poisson distribution to model the mean behavior of count data, excels in scenarios of severe overdispersion. Conversely, the GMERF performs best under conditions where Poisson distribution assumptions are moderately met. In a case study using real-world data from the state of Guerrero, Mexico, the proposed methods effectively estimate area-level means while capturing the uncertainty inherent in overdispersed count data. These findings highlight their practical applicability for small area estimation.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"211 ","pages":"Article 108218"},"PeriodicalIF":1.5,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144196139","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 : 2025-05-23DOI: 10.1016/j.csda.2025.108208
Yichun Song
A Frisch-Waugh-Lovell-type (FWL) theorem for empirical likelihood estimation with instrumental variables is presented, which resembles the standard FWL theorem in ordinary least squares (OLS), but its partitioning procedure employs the empirical likelihood weights at the solution rather than the original sample distribution. This result is leveraged to simplify the computational process through an iterative algorithm, where exogenous variables are partitioned out using weighted least squares, and the weights are updated between iterations. Furthermore, it is demonstrated that iterations converge locally to the original empirical likelihood estimate at a stochastically super-linear rate. A feasible iterative constrained optimization algorithm for calculating empirical-likelihood-based confidence intervals is provided, along with a discussion of its properties. Monte Carlo simulations indicate that the iterative algorithm is robust and produces results within the numerical tolerance of the original empirical likelihood estimator in finite samples, while significantly improves computation in large-scale problems. Additionally, the algorithm performs effectively in an illustrative application using the return to education framework.
{"title":"A Frisch-Waugh-Lovell theorem for empirical likelihood","authors":"Yichun Song","doi":"10.1016/j.csda.2025.108208","DOIUrl":"10.1016/j.csda.2025.108208","url":null,"abstract":"<div><div>A Frisch-Waugh-Lovell-type (FWL) theorem for empirical likelihood estimation with instrumental variables is presented, which resembles the standard FWL theorem in ordinary least squares (OLS), but its partitioning procedure employs the empirical likelihood weights at the solution rather than the original sample distribution. This result is leveraged to simplify the computational process through an iterative algorithm, where exogenous variables are partitioned out using weighted least squares, and the weights are updated between iterations. Furthermore, it is demonstrated that iterations converge locally to the original empirical likelihood estimate at a stochastically super-linear rate. A feasible iterative constrained optimization algorithm for calculating empirical-likelihood-based confidence intervals is provided, along with a discussion of its properties. Monte Carlo simulations indicate that the iterative algorithm is robust and produces results within the numerical tolerance of the original empirical likelihood estimator in finite samples, while significantly improves computation in large-scale problems. Additionally, the algorithm performs effectively in an illustrative application using the return to education framework.</div></div>","PeriodicalId":55225,"journal":{"name":"Computational Statistics & Data Analysis","volume":"211 ","pages":"Article 108208"},"PeriodicalIF":1.5,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144137907","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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