Xingcai Zhou, Dehan Kong, Matthew Pietrosanu, Linglong Kong, R. Karunamuni
This work is motivated by a gap in the functional data analysis literature, particularly in the context of neuroimaging, regarding the ability of functional models to robustly accommodate intra‐observation dependence. In response, we propose an M‐estimator based on generalized empirical likelihood for the varying‐coefficient model with a functional response. We develop statistical inference procedures, simultaneous confidence regions, and a global general linear hypothesis test for the model's functional coefficient. Our theoretical results establish the weak convergence of the log‐likelihood ratio process, a nonparametric version of Wilks' theorem for the log‐likelihood ratio, and asymptotic properties of the proposed estimator. Through a simulation study, we show that the proposed confidence sets have close‐to‐nominal coverage probabilities. In a real‐world application to a neuroimaging dataset, we show that mini‐mental state examination score and apolipoprotein E genotype have significant associations with fractional anisotropy, while associations with gender and age are only present at high quantile levels.
这项工作的灵感来自于功能数据分析文献中的一个空白，尤其是在神经成像方面，即功能模型能否稳健地适应观测内依赖性。为此，我们提出了一种基于广义经验似然的 M-估计器，用于具有功能响应的变化系数模型。我们为模型的函数系数开发了统计推断程序、同步置信区和全局一般线性假设检验。我们的理论结果确定了对数似然比过程的弱收敛性、对数似然比的非参数版本 Wilks' theorem 以及所建议估计器的渐近特性。通过模拟研究，我们证明了所提出的置信集具有接近名义的覆盖概率。在神经影像数据集的实际应用中，我们发现迷你精神状态检查得分和载脂蛋白 E 基因型与分数各向异性有显著的关联，而与性别和年龄的关联只存在于高量级水平。
{"title":"Empirical likelihood M‐estimation for the varying‐coefficient model with functional response","authors":"Xingcai Zhou, Dehan Kong, Matthew Pietrosanu, Linglong Kong, R. Karunamuni","doi":"10.1111/sjos.12717","DOIUrl":"https://doi.org/10.1111/sjos.12717","url":null,"abstract":"This work is motivated by a gap in the functional data analysis literature, particularly in the context of neuroimaging, regarding the ability of functional models to robustly accommodate intra‐observation dependence. In response, we propose an M‐estimator based on generalized empirical likelihood for the varying‐coefficient model with a functional response. We develop statistical inference procedures, simultaneous confidence regions, and a global general linear hypothesis test for the model's functional coefficient. Our theoretical results establish the weak convergence of the log‐likelihood ratio process, a nonparametric version of Wilks' theorem for the log‐likelihood ratio, and asymptotic properties of the proposed estimator. Through a simulation study, we show that the proposed confidence sets have close‐to‐nominal coverage probabilities. In a real‐world application to a neuroimaging dataset, we show that mini‐mental state examination score and apolipoprotein E genotype have significant associations with fractional anisotropy, while associations with gender and age are only present at high quantile levels.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140675173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Arellano-Valle, Javier E. Contreras‐Reyes, M. Genton
{"title":"Corrigendum to “Shannon Entropy and Mutual Information for Multivariate Skew‐Elliptical Distributions” published in Scandinavian Journal of Statistics (2013), vol. 40, pp. 42–62","authors":"R. Arellano-Valle, Javier E. Contreras‐Reyes, M. Genton","doi":"10.1111/sjos.12718","DOIUrl":"https://doi.org/10.1111/sjos.12718","url":null,"abstract":"","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140674230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In survival analysis, cure models have been developed to account for the presence of cured subjects that will never experience the event of interest. Mixture cure models with a parametric model for the incidence and a semiparametric model for the survival of the susceptibles are particularly common in practice. Because of the latent cure status, maximum likelihood estimation is performed via the iterative EM algorithm. Here, we focus on the cure probabilities and propose a two‐step procedure to improve upon the maximum likelihood estimator when the sample size is not large. The new method is based on presmoothing by first constructing a nonparametric estimator and then projecting it on the desired parametric class. We investigate the theoretical properties of the resulting estimator and show through an extensive simulation study for the logistic‐Cox model that it outperforms the existing method. Practical use of the method is illustrated through two melanoma datasets.
在生存分析中，人们开发了治愈模型，以考虑到永远不会发生相关事件的治愈受试者的存在。在实践中，采用发病率参数模型和易感人群生存率半参数模型的混合治愈模型尤为常见。由于存在潜伏的治愈状态，最大似然估计是通过迭代 EM 算法进行的。在此，我们将重点放在治愈概率上，并提出了一个两步程序，以改进样本量不大时的最大似然估计方法。新方法基于预平滑，首先构建一个非参数估计器，然后将其投影到所需的参数类别上。我们研究了由此产生的估计器的理论特性，并通过对 logistic-Cox 模型的大量模拟研究表明，它优于现有方法。我们通过两个黑色素瘤数据集说明了该方法的实际应用。
{"title":"A two‐step estimation procedure for semiparametric mixture cure models","authors":"Eni Musta, Valentin Patilea, Ingrid Van Keilegom","doi":"10.1111/sjos.12713","DOIUrl":"https://doi.org/10.1111/sjos.12713","url":null,"abstract":"In survival analysis, cure models have been developed to account for the presence of cured subjects that will never experience the event of interest. Mixture cure models with a parametric model for the incidence and a semiparametric model for the survival of the susceptibles are particularly common in practice. Because of the latent cure status, maximum likelihood estimation is performed via the iterative EM algorithm. Here, we focus on the cure probabilities and propose a two‐step procedure to improve upon the maximum likelihood estimator when the sample size is not large. The new method is based on presmoothing by first constructing a nonparametric estimator and then projecting it on the desired parametric class. We investigate the theoretical properties of the resulting estimator and show through an extensive simulation study for the logistic‐Cox model that it outperforms the existing method. Practical use of the method is illustrated through two melanoma datasets.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140624872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is about the modeling of cumulative hazard functions using martingale posterior distributions. The focus is on uncertainty quantification from a nonparametric perspective. The foundational Bayesian model in this case is the beta process and the classic estimator is the Nelson–Aalen. We use a sequence of estimators which form a martingale in order to obtain a random cumulative hazard function from the martingale posterior. The connection with the beta process is established and a number of illustrations is presented.
{"title":"Martingale posterior distributions for cumulative hazard functions","authors":"Stephen G. Walker","doi":"10.1111/sjos.12712","DOIUrl":"https://doi.org/10.1111/sjos.12712","url":null,"abstract":"This paper is about the modeling of cumulative hazard functions using martingale posterior distributions. The focus is on uncertainty quantification from a nonparametric perspective. The foundational Bayesian model in this case is the beta process and the classic estimator is the Nelson–Aalen. We use a sequence of estimators which form a martingale in order to obtain a random cumulative hazard function from the martingale posterior. The connection with the beta process is established and a number of illustrations is presented.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with a Skorokhod's integral‐based least squares‐ (LS) type estimator of the drift parameter computed from multiple (possibly dependent) copies of the solution of a stochastic differential equation (SDE) driven by a fractional Brownian motion of Hurst index . On the one hand, some convergence results are established on our LS estimator when . On the other hand, when , Skorokhod's integral‐based estimators cannot be computed from data, but in this paper some convergence results are established on a computable approximation of our LS estimator.
本文论述了一种基于斯科洛克霍德积分的最小二乘法（LS）型漂移参数估计器，该估计器由赫斯特指数为.的分数布朗运动驱动的随机微分方程（SDE）解的多个（可能依赖的）副本计算得出。一方面，当......时，我们的 LS 估计器建立了一些收敛结果。另一方面，当 , 时，Skorokhod 基于积分的估计器无法从数据中计算出来，但本文对我们的 LS 估计器的可计算近似值建立了一些收敛结果。
{"title":"On a computable Skorokhod's integral‐based estimator of the drift parameter in fractional SDE","authors":"Nicolas Marie","doi":"10.1111/sjos.12711","DOIUrl":"https://doi.org/10.1111/sjos.12711","url":null,"abstract":"This paper deals with a Skorokhod's integral‐based least squares‐ (LS) type estimator of the drift parameter computed from multiple (possibly dependent) copies of the solution of a stochastic differential equation (SDE) driven by a fractional Brownian motion of Hurst index . On the one hand, some convergence results are established on our LS estimator when . On the other hand, when , Skorokhod's integral‐based estimators cannot be computed from data, but in this paper some convergence results are established on a computable approximation of our LS estimator.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies generative adversarial networks (GANs) from the perspective of statistical inference. A GAN is a popular machine learning method in which the parameters of two neural networks, a generator and a discriminator, are estimated to solve a particular minimax problem. This minimax problem typically has a multitude of solutions and the focus of this paper are the statistical properties of these solutions. We address two key statistical issues for the generator and discriminator network parameters, consistent estimation and confidence sets. We first show that the set of solutions to the sample GAN problem is a (Hausdorff) consistent estimator of the set of solutions to the corresponding population GAN problem. We then devise a computationally intensive procedure to form confidence sets and show that these sets contain the population GAN solutions with the desired coverage probability. Small numerical experiments and a Monte Carlo study illustrate our results and verify our theoretical findings. We also show that our results apply in general minimax problems that may be nonconvex, nonconcave, and have multiple solutions.
本文从统计推断的角度研究生成对抗网络（GAN）。生成式对抗网络（GAN）是一种流行的机器学习方法，通过估算生成器和判别器这两个神经网络的参数来解决一个特定的最小问题。这个最小问题通常有多种解决方案，本文的重点是这些解决方案的统计特性。我们探讨了生成器和判别器网络参数的两个关键统计问题：一致估计和置信集。我们首先证明，样本 GAN 问题的解集是相应群体 GAN 问题解集的（豪斯多夫）一致性估计。然后，我们设计了一种计算密集型程序来形成置信集，并证明这些置信集包含具有所需覆盖概率的群体 GAN 解。小型数值实验和蒙特卡罗研究说明了我们的结果，并验证了我们的理论发现。我们还证明，我们的结果适用于一般的最小问题，这些问题可能是非凸、非凹和多解的。
{"title":"Statistical inference for generative adversarial networks and other minimax problems","authors":"Mika Meitz","doi":"10.1111/sjos.12710","DOIUrl":"https://doi.org/10.1111/sjos.12710","url":null,"abstract":"This paper studies generative adversarial networks (GANs) from the perspective of statistical inference. A GAN is a popular machine learning method in which the parameters of two neural networks, a generator and a discriminator, are estimated to solve a particular minimax problem. This minimax problem typically has a multitude of solutions and the focus of this paper are the statistical properties of these solutions. We address two key statistical issues for the generator and discriminator network parameters, consistent estimation and confidence sets. We first show that the set of solutions to the sample GAN problem is a (Hausdorff) consistent estimator of the set of solutions to the corresponding population GAN problem. We then devise a computationally intensive procedure to form confidence sets and show that these sets contain the population GAN solutions with the desired coverage probability. Small numerical experiments and a Monte Carlo study illustrate our results and verify our theoretical findings. We also show that our results apply in general minimax problems that may be nonconvex, nonconcave, and have multiple solutions.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-01Epub Date: 2023-08-07DOI: 10.1111/sjos.12685
Rui Duan, C Jason Liang, Pamela A Shaw, Cheng Yong Tang, Yong Chen
Practical problems with missing data are common, and many methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism governing data missingness, and correctly deciding the appropriate mechanism is crucially relevant for conducting proper practical investigations. In this paper, we present a new hypothesis testing approach for deciding between the conventional notions of missing at random and missing not at random in generalized linear models in the presence of instrumental variables. The foundational idea is to develop appropriate discrepancy measures between estimators whose properties significantly differ only when missing at random does not hold. We show that our testing approach achieves an objective data-oriented choice between missing at random or not. We demonstrate the feasibility, validity, and efficacy of the new test by theoretical analysis, simulation studies, and a real data analysis.
{"title":"Testing the missing at random assumption in generalized linear models in the presence of instrumental variables.","authors":"Rui Duan, C Jason Liang, Pamela A Shaw, Cheng Yong Tang, Yong Chen","doi":"10.1111/sjos.12685","DOIUrl":"10.1111/sjos.12685","url":null,"abstract":"<p><p>Practical problems with missing data are common, and many methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism governing data missingness, and correctly deciding the appropriate mechanism is crucially relevant for conducting proper practical investigations. In this paper, we present a new hypothesis testing approach for deciding between the conventional notions of missing at random and missing not at random in generalized linear models in the presence of instrumental variables. The foundational idea is to develop appropriate discrepancy measures between estimators whose properties significantly differ only when missing at random does not hold. We show that our testing approach achieves an objective data-oriented choice between missing at random or not. We demonstrate the feasibility, validity, and efficacy of the new test by theoretical analysis, simulation studies, and a real data analysis.</p>","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10871667/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46657247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our analysis is that the stochastic integral part is unobserved and nonparametric. Additionally, the drift may depend on the (unknown and unobserved) stochastic integrand. Our results hold for ergodic semi-parametric diffusions and backward SDEs. Simulation studies confirm that the methods proposed yield good convergence results.
{"title":"Efficient drift parameter estimation for ergodic solutions of backward SDEs","authors":"Teppei Ogihara, Mitja Stadje","doi":"10.1111/sjos.12709","DOIUrl":"https://doi.org/10.1111/sjos.12709","url":null,"abstract":"We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our analysis is that the stochastic integral part is unobserved and nonparametric. Additionally, the drift may depend on the (unknown and unobserved) stochastic integrand. Our results hold for ergodic semi-parametric diffusions and backward SDEs. Simulation studies confirm that the methods proposed yield good convergence results.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies the autoregressive and moving average (ARMA) model with time-functional variance (TFV) noises, called the ARMA-TFV model. We first establish the consistency and asymptotic normality of its least squares estimator (LSE). The Wald tests and portmanteau tests are constructed based on the theory for variable selection and model checking. A simulation study is carried out to assess the performance of our approach in finite samples, and two real examples are given. It should be mentioned that the process generated from the ARMA-TFV model is not stationary, and the technique in this paper is nonstandard and may provide insights for future research in this area.
{"title":"Asymptotic inference of the ARMA model with time-functional variance noises","authors":"Bibi Cai, Enwen Zhu, Shiqing Ling","doi":"10.1111/sjos.12708","DOIUrl":"https://doi.org/10.1111/sjos.12708","url":null,"abstract":"This paper studies the autoregressive and moving average (ARMA) model with time-functional variance (TFV) noises, called the ARMA-TFV model. We first establish the consistency and asymptotic normality of its least squares estimator (LSE). The Wald tests and portmanteau tests are constructed based on the theory for variable selection and model checking. A simulation study is carried out to assess the performance of our approach in finite samples, and two real examples are given. It should be mentioned that the process generated from the ARMA-TFV model is not stationary, and the technique in this paper is nonstandard and may provide insights for future research in this area.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many matrix‐valued functions of an Wishart matrix , , say, are homogeneous of degree in , and are equivariant under the conjugate action of the orthogonal group , that is, , . It is easy to see that the expectation of such a function is itself homogeneous of degree in , the covariance matrix, and are also equivariant under the action of on . The space of such homogeneous, equivariant, matrix‐valued functions is spanned by elements of the type , where and, for each , varies over the partitions of , and denotes the power‐sum symmetric function indexed by . In the analogous case where is replaced by , these elements are replaced by . In this paper, we derive recurrence relations and analytical expressions for the expectations of such functions. Our results provide highly efficient methods for the computation of all such moments.
{"title":"On the expectations of equivariant matrix‐valued functions of Wishart and inverse Wishart matrices","authors":"Grant Hillier, Raymond M. Kan","doi":"10.1111/sjos.12707","DOIUrl":"https://doi.org/10.1111/sjos.12707","url":null,"abstract":"Many matrix‐valued functions of an Wishart matrix , , say, are homogeneous of degree in , and are equivariant under the conjugate action of the orthogonal group , that is, , . It is easy to see that the expectation of such a function is itself homogeneous of degree in , the covariance matrix, and are also equivariant under the action of on . The space of such homogeneous, equivariant, matrix‐valued functions is spanned by elements of the type , where and, for each , varies over the partitions of , and denotes the power‐sum symmetric function indexed by . In the analogous case where is replaced by , these elements are replaced by . In this paper, we derive recurrence relations and analytical expressions for the expectations of such functions. Our results provide highly efficient methods for the computation of all such moments.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140483369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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