Pub Date : 2026-07-01Epub Date: 2025-11-27DOI: 10.1016/j.jspi.2025.106369
Guanfu Liu , Yuejiao Fu
The finite mixtures of multivariate Poisson (FMMP) distributions have wide applications in the real world. Testing for homogeneity under the FMMP models is important, however, there is no generic solution to this problem as far as we know. In this paper, we propose an EM-test for homogeneity under the FMMP models to fulfill the gap. We establish the strong consistency of the maximum likelihood estimator for the mixing distribution by relaxing two conditions required in existing literature. The null limiting distribution of the proposed test is studied, and based on the limiting distribution, a resampling procedure is constructed to approximate the -value of the test. The loss of the strong identifiability for the multivariate Poisson distribution poses a significant challenge in deriving the null limiting distribution. Finally, simulation studies and real-data analysis demonstrate the good performance of the proposed test.
{"title":"Homogeneity testing under finite mixtures of multivariate Poisson distributions","authors":"Guanfu Liu , Yuejiao Fu","doi":"10.1016/j.jspi.2025.106369","DOIUrl":"10.1016/j.jspi.2025.106369","url":null,"abstract":"<div><div>The finite mixtures of multivariate Poisson (FMMP) distributions have wide applications in the real world. Testing for homogeneity under the FMMP models is important, however, there is no generic solution to this problem as far as we know. In this paper, we propose an EM-test for homogeneity under the FMMP models to fulfill the gap. We establish the strong consistency of the maximum likelihood estimator for the mixing distribution by relaxing two conditions required in existing literature. The null limiting distribution of the proposed test is studied, and based on the limiting distribution, a resampling procedure is constructed to approximate the <span><math><mi>p</mi></math></span>-value of the test. The loss of the strong identifiability for the multivariate Poisson distribution poses a significant challenge in deriving the null limiting distribution. Finally, simulation studies and real-data analysis demonstrate the good performance of the proposed test.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"243 ","pages":"Article 106369"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145610584","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 : 2026-07-01Epub Date: 2026-01-20DOI: 10.1016/j.jspi.2026.106379
Satya Prakash Singh , Ori Davidov
In many experimental settings, the primary focus is the comparisons of pairs of treatments. This paper addresses the problem of optimally allocating experimental units to treatment groups when responses are binary. The proposed approach employs a power-based max–min approach that identifies the optimal experimental design in various experimental settings.
{"title":"Max–min experimental designs for comparing pairs of treatments with binary outcomes","authors":"Satya Prakash Singh , Ori Davidov","doi":"10.1016/j.jspi.2026.106379","DOIUrl":"10.1016/j.jspi.2026.106379","url":null,"abstract":"<div><div>In many experimental settings, the primary focus is the comparisons of pairs of treatments. This paper addresses the problem of optimally allocating experimental units to treatment groups when responses are binary. The proposed approach employs a power-based max–min approach that identifies the optimal experimental design in various experimental settings.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"243 ","pages":"Article 106379"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146023068","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 : 2026-05-01Epub Date: 2025-10-28DOI: 10.1016/j.jspi.2025.106358
Sumito Kurata, Kei Hirose
Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the data and phenomenon, we need to determine an adequate value of the regularization parameter. Regarding the determination of the regularization parameter in the linear regression model, we often apply the information criteria like the AIC and BIC, however, it has been pointed out that these criteria are sensitive to outliers and tend not to perform well in high-dimensional settings. Outliers generally have a negative effect on not only estimation but also model selection, consequently, it is important to employ a selection method with robustness against outliers. In addition, when the number of explanatory variables is quite large, most conventional criteria are prone to select unnecessary explanatory variables. In this paper, we propose model evaluation criteria based on the statistical divergence with excellence in robustness in both of parametric estimation and model selection, by applying the quasi-Bayesian procedure. Our proposed criteria achieve the selection consistency even in high-dimensional settings due to precise approximation, simultaneously with robustness. We also investigate the conditions for establishing robustness and consistency, and provide an appropriate example of the divergence and penalty term that can achieve the desirable properties. We finally report the results of some numerical examples to verify that the proposed criteria perform robust and consistent variable selection compared with the conventional selection methods.
{"title":"Robust and consistent model evaluation criteria in high-dimensional regression","authors":"Sumito Kurata, Kei Hirose","doi":"10.1016/j.jspi.2025.106358","DOIUrl":"10.1016/j.jspi.2025.106358","url":null,"abstract":"<div><div>Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the data and phenomenon, we need to determine an adequate value of the regularization parameter. Regarding the determination of the regularization parameter in the linear regression model, we often apply the information criteria like the AIC and BIC, however, it has been pointed out that these criteria are sensitive to outliers and tend not to perform well in high-dimensional settings. Outliers generally have a negative effect on not only estimation but also model selection, consequently, it is important to employ a selection method with robustness against outliers. In addition, when the number of explanatory variables is quite large, most conventional criteria are prone to select unnecessary explanatory variables. In this paper, we propose model evaluation criteria based on the statistical divergence with excellence in robustness in both of parametric estimation and model selection, by applying the quasi-Bayesian procedure. Our proposed criteria achieve the selection consistency even in high-dimensional settings due to precise approximation, simultaneously with robustness. We also investigate the conditions for establishing robustness and consistency, and provide an appropriate example of the divergence and penalty term that can achieve the desirable properties. We finally report the results of some numerical examples to verify that the proposed criteria perform robust and consistent variable selection compared with the conventional selection methods.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"242 ","pages":"Article 106358"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145415645","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 : 2026-05-01Epub Date: 2025-09-02DOI: 10.1016/j.jspi.2025.106338
Sijie Zheng , Xiaojun Song
A nonparametric test is developed to determine whether the trend of a partially linear model (PLM) with dependent errors and locally stationary regressors follows a specific parametric form. The test is asymptotically normal under the null hypothesis of correct trend specification and is consistent against various alternatives that deviate from the null hypothesis. The testing power against two classes of local alternatives approaching the null at different rates is derived, along with the asymptotic distribution of the test under fixed alternatives. We also propose a wild bootstrap procedure to better approximate the finite sample null distribution of the test. Statistical inference is performed on the trend specification in the Phillips curve and ozone concentration.
{"title":"Inference for trend functions in partially linear models","authors":"Sijie Zheng , Xiaojun Song","doi":"10.1016/j.jspi.2025.106338","DOIUrl":"10.1016/j.jspi.2025.106338","url":null,"abstract":"<div><div>A nonparametric test is developed to determine whether the trend of a partially linear model (PLM) with dependent errors and locally stationary regressors follows a specific parametric form. The test is asymptotically normal under the null hypothesis of correct trend specification and is consistent against various alternatives that deviate from the null hypothesis. The testing power against two classes of local alternatives approaching the null at different rates is derived, along with the asymptotic distribution of the test under fixed alternatives. We also propose a wild bootstrap procedure to better approximate the finite sample null distribution of the test. Statistical inference is performed on the trend specification in the Phillips curve and ozone concentration.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"242 ","pages":"Article 106338"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145004499","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 : 2026-05-01Epub Date: 2025-09-27DOI: 10.1016/j.jspi.2025.106354
Yanbo Pei, Xiaoxiao Ren, Baoxue Zhang
The problem of testing the equality of k-sample mean vectors with different covariance matrices, known as the Behrens-Fisher (BF) problem for k-sample, is a significant issue in statistics. Hu and Bai (2017) proposed a test statistic that operates under a factor-like model structure assumption and demonstrated its normal limit. Building on this work, we further explore the asymptotic properties of the test statistic. We prove that the asymptotic null distribution of the test statistic is a Chi-square-type mixture distribution under a model-free assumption and establish its asymptotic power under a full alternative hypothesis. Moreover, we show that the asymptotic null distribution of the test statistic is either normal or a weighted sum of normal and Chi-square random variables, depending on the convergence rate of the eigenvalues of the covariance matrix with model free assumption. To address practical challenges in high-dimensional data, we propose a new weighted bootstrap procedure that is simple to implement. Simulation studies demonstrate that our proposed test procedure outperforms existing methods in terms of size control under various settings. Furthermore, real data applications illustrate the applicability of our test procedure to a variety of high-dimensional data analysis problems.
{"title":"The k-sample Behrens-Fisher problem for high-dimensional data with model free assumption","authors":"Yanbo Pei, Xiaoxiao Ren, Baoxue Zhang","doi":"10.1016/j.jspi.2025.106354","DOIUrl":"10.1016/j.jspi.2025.106354","url":null,"abstract":"<div><div>The problem of testing the equality of <em>k</em>-sample mean vectors with different covariance matrices, known as the Behrens-Fisher (BF) problem for <em>k</em>-sample, is a significant issue in statistics. Hu and Bai (2017) proposed a test statistic that operates under a factor-like model structure assumption and demonstrated its normal limit. Building on this work, we further explore the asymptotic properties of the test statistic. We prove that the asymptotic null distribution of the test statistic is a Chi-square-type mixture distribution under a model-free assumption and establish its asymptotic power under a full alternative hypothesis. Moreover, we show that the asymptotic null distribution of the test statistic is either normal or a weighted sum of normal and Chi-square random variables, depending on the convergence rate of the eigenvalues of the covariance matrix with model free assumption. To address practical challenges in high-dimensional data, we propose a new weighted bootstrap procedure that is simple to implement. Simulation studies demonstrate that our proposed test procedure outperforms existing methods in terms of size control under various settings. Furthermore, real data applications illustrate the applicability of our test procedure to a variety of high-dimensional data analysis problems.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"242 ","pages":"Article 106354"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220648","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 : 2026-05-01Epub Date: 2025-09-19DOI: 10.1016/j.jspi.2025.106350
Raul Matsushita , Gabriel Gomes , Regina Da Fonseca , Eduardo Nakano , Roberto Vila
We present the Rényi divergence as a statistic for assessing goodness-of-fit in sparse frequency tables, where small expected counts can undermine the reliability of the traditional chi-square test. The Rényi divergence with index in (0,1) is a natural choice because it circumvents division-related issues by small frequencies. Our main result demonstrates that the Rényi statistic asymptotically follows a chi-square distribution. Through theoretical insights and Monte Carlo simulations, we evaluate the performance of the Rényi statistic across various values of the divergence index. We find that smaller index values improve the alignment of the Rényi statistic with the chi-square distribution and enhance its performance in sparse data settings. Additionally, the Rényi statistic exhibits good power properties in detecting deviations from the null hypothesis under these conditions. To illustrate its practical applicability, we present two real-world data analyses, highlighting the robustness of the Rényi divergence in scenarios involving sparse categories.
{"title":"Assessing goodness-of-fit for sparse categories using Rényi divergence","authors":"Raul Matsushita , Gabriel Gomes , Regina Da Fonseca , Eduardo Nakano , Roberto Vila","doi":"10.1016/j.jspi.2025.106350","DOIUrl":"10.1016/j.jspi.2025.106350","url":null,"abstract":"<div><div>We present the Rényi divergence as a statistic for assessing goodness-of-fit in sparse frequency tables, where small expected counts can undermine the reliability of the traditional chi-square test. The Rényi divergence with index in (0,1) is a natural choice because it circumvents division-related issues by small frequencies. Our main result demonstrates that the Rényi statistic asymptotically follows a chi-square distribution. Through theoretical insights and Monte Carlo simulations, we evaluate the performance of the Rényi statistic across various values of the divergence index. We find that smaller index values improve the alignment of the Rényi statistic with the chi-square distribution and enhance its performance in sparse data settings. Additionally, the Rényi statistic exhibits good power properties in detecting deviations from the null hypothesis under these conditions. To illustrate its practical applicability, we present two real-world data analyses, highlighting the robustness of the Rényi divergence in scenarios involving sparse categories.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"242 ","pages":"Article 106350"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105738","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 : 2026-05-01Epub Date: 2025-10-21DOI: 10.1016/j.jspi.2025.106356
Samuel Onyambu, Hongquan Xu
Space-filling designs are extensively used in computer experiments to analyze complex systems. Among these, uniform projection designs stand out for their desirable low-dimensional projection properties and robustness against other criteria. However, no efficient algorithm currently exists for generating such designs. This study explores the construction of uniform projection designs using a differential evolution (DE) algorithm. DE, an evolutionary algorithm, is known for its simplicity, robustness, and effectiveness in solving complex optimization problems, though its performance is highly sensitive to several hyperparameters. Our goal is to investigate the structure of the hyperparameter space, evaluate the contribution of each hyperparameter, and provide guidelines for optimal hyperparameter settings across various scenarios. To achieve this, we conduct a comprehensive comparison of different experimental designs and surrogate models.
{"title":"Tuning differential evolution algorithm for constructing uniform projection designs","authors":"Samuel Onyambu, Hongquan Xu","doi":"10.1016/j.jspi.2025.106356","DOIUrl":"10.1016/j.jspi.2025.106356","url":null,"abstract":"<div><div>Space-filling designs are extensively used in computer experiments to analyze complex systems. Among these, uniform projection designs stand out for their desirable low-dimensional projection properties and robustness against other criteria. However, no efficient algorithm currently exists for generating such designs. This study explores the construction of uniform projection designs using a differential evolution (DE) algorithm. DE, an evolutionary algorithm, is known for its simplicity, robustness, and effectiveness in solving complex optimization problems, though its performance is highly sensitive to several hyperparameters. Our goal is to investigate the structure of the hyperparameter space, evaluate the contribution of each hyperparameter, and provide guidelines for optimal hyperparameter settings across various scenarios. To achieve this, we conduct a comprehensive comparison of different experimental designs and surrogate models.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"242 ","pages":"Article 106356"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145362408","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 : 2026-05-01Epub Date: 2025-09-06DOI: 10.1016/j.jspi.2025.106337
Jiangyan Wang, Yang Ren, Jinguan Lin
Covariance estimation poses a crucial challenge in high-dimensional data analysis, especially when traditional methods (e.g., sample covariance) are inaccurate, particularly with small sample sizes. A promising solution is to exploit inherent data structures such as low-rankness, sparsity, or smoothness. For tensor data (multi-dimensional arrays), structured regularization aids in dimensionality reduction. This paper introduces novel regularization methods for tensor covariance estimation, specifically applying banded and tapering structures to the covariance matrix. We use Kronecker Product Canonical Polyadic (KPCP) decomposition to approximate large matrices via the Kronecker product of smaller matrices. A split resampling scheme is employed to select parameters for the KPCP decomposition from noisy data. This leads to two methods: KPCP-TB-R (Triply Banded-Resampling) and KPCP-TT-R (Triply Tapering-Resampling). Additionally, sparse (thresholding) and multi-structured regularization approaches are introduced for comparison. The effectiveness and robustness of the proposed methods are validated through extensive simulations and applied to monthly export trade volume data.
{"title":"Structured regularization covariance estimation in tensor-valued data analysis","authors":"Jiangyan Wang, Yang Ren, Jinguan Lin","doi":"10.1016/j.jspi.2025.106337","DOIUrl":"10.1016/j.jspi.2025.106337","url":null,"abstract":"<div><div>Covariance estimation poses a crucial challenge in high-dimensional data analysis, especially when traditional methods (e.g., sample covariance) are inaccurate, particularly with small sample sizes. A promising solution is to exploit inherent data structures such as low-rankness, sparsity, or smoothness. For tensor data (multi-dimensional arrays), structured regularization aids in dimensionality reduction. This paper introduces novel regularization methods for tensor covariance estimation, specifically applying banded and tapering structures to the covariance matrix. We use Kronecker Product Canonical Polyadic (KPCP) decomposition to approximate large matrices via the Kronecker product of smaller matrices. A split resampling scheme is employed to select parameters for the KPCP decomposition from noisy data. This leads to two methods: KPCP-TB-R (Triply Banded-Resampling) and KPCP-TT-R (Triply Tapering-Resampling). Additionally, sparse (thresholding) and multi-structured regularization approaches are introduced for comparison. The effectiveness and robustness of the proposed methods are validated through extensive simulations and applied to monthly export trade volume data.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"242 ","pages":"Article 106337"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049542","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 : 2026-05-01Epub Date: 2025-09-24DOI: 10.1016/j.jspi.2025.106349
Tian-fang Zhang , Yue-ru Yan , Fasheng Sun
Orthogonal Latin hypercube designs are widely used in computer experiments because of their attractive properties. In this article, we develop a new grouping method to construct such designs. Compared to the existing results, the new constructed designs can accommodate more factors with the same runsize, which means they are more cost-effective. Moreover, the resulting designs possess not only orthogonality, but also appealing space-filling properties in low dimensions, which make them very suitable for computer experiments.
{"title":"Orthogonal Latin hypercube designs with hidden low-dimensional projection","authors":"Tian-fang Zhang , Yue-ru Yan , Fasheng Sun","doi":"10.1016/j.jspi.2025.106349","DOIUrl":"10.1016/j.jspi.2025.106349","url":null,"abstract":"<div><div>Orthogonal Latin hypercube designs are widely used in computer experiments because of their attractive properties. In this article, we develop a new grouping method to construct such designs. Compared to the existing results, the new constructed designs can accommodate more factors with the same runsize, which means they are more cost-effective. Moreover, the resulting designs possess not only orthogonality, but also appealing space-filling properties in low dimensions, which make them very suitable for computer experiments.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"242 ","pages":"Article 106349"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220650","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 : 2026-05-01Epub Date: 2025-09-22DOI: 10.1016/j.jspi.2025.106351
Yibo Yan , Xiaozhou Wang , Riquan Zhang
In this paper, we propose a class of estimators based on the robust and computationally efficient gradient estimation for both low- and high-dimensional risk minimization framework. The gradient estimation in this work is constructed using a series of newly proposed univariate robust and efficient mean estimators. Our proposed estimators are obtained iteratively using a variant of the gradient descent method, where the update direction is determined by a robust and computationally efficient gradient. These estimators not only have explicit expressions and can be obtained through arithmetic operations but are also robust to arbitrary outliers in common statistical models. Theoretically, we establish the convergence of the algorithms and derive non-asymptotic error bounds for these iterative estimators. Specifically, we apply our methods to linear and logistic regression models, achieving robust parameter estimates and corresponding excess risk bounds. Unlike previous work, our theoretical results rely on a magnitude function of the outliers, which captures the extent of their deviation from the inliers. Finally, we present extensive simulation experiments on both low- and high-dimensional linear models to demonstrate the superior performance of our proposed estimators compared to several baseline methods.
{"title":"Robust and computationally efficient gradient-based estimation","authors":"Yibo Yan , Xiaozhou Wang , Riquan Zhang","doi":"10.1016/j.jspi.2025.106351","DOIUrl":"10.1016/j.jspi.2025.106351","url":null,"abstract":"<div><div>In this paper, we propose a class of estimators based on the robust and computationally efficient gradient estimation for both low- and high-dimensional risk minimization framework. The gradient estimation in this work is constructed using a series of newly proposed univariate robust and efficient mean estimators. Our proposed estimators are obtained iteratively using a variant of the gradient descent method, where the update direction is determined by a robust and computationally efficient gradient. These estimators not only have explicit expressions and can be obtained through arithmetic operations but are also robust to arbitrary outliers in common statistical models. Theoretically, we establish the convergence of the algorithms and derive non-asymptotic error bounds for these iterative estimators. Specifically, we apply our methods to linear and logistic regression models, achieving robust parameter estimates and corresponding excess risk bounds. Unlike previous work, our theoretical results rely on a magnitude function of the outliers, which captures the extent of their deviation from the inliers. Finally, we present extensive simulation experiments on both low- and high-dimensional linear models to demonstrate the superior performance of our proposed estimators compared to several baseline methods.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"242 ","pages":"Article 106351"},"PeriodicalIF":0.8,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158353","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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