Pub Date : 2025-07-01Epub Date: 2024-11-19DOI: 10.1016/j.jspi.2024.106250
Abbas Khalili , Archer Yi Yang , Xiaonan Da
Mixture-of-experts provide flexible statistical models for a wide range of regression (supervised learning) problems. Often a large number of covariates (features) are available in many modern applications yet only a small subset of them is useful in explaining a response variable of interest. This calls for a feature selection device. In this paper, we present new group-feature selection and estimation methods for sparse mixture-of-experts models when the number of features can be nearly comparable to the sample size. We prove the consistency of the methods in both parameter estimation and feature selection. We implement the methods using a modified EM algorithm combined with proximal gradient method which results in a convenient closed-form parameter update in the M-step of the algorithm. We examine the finite-sample performance of the methods through simulations, and demonstrate their applications in a real data example on exploring relationships in body measurements.
专家混合模型为各种回归（监督学习）问题提供了灵活的统计模型。在许多现代应用中，往往会有大量的协变量（特征），但其中只有一小部分对解释感兴趣的响应变量有用。这就需要一种特征选择装置。在本文中，我们针对稀疏专家混合物模型提出了新的分组特征选择和估计方法，当特征数量几乎与样本大小相当时，就可以使用这种方法。我们证明了这些方法在参数估计和特征选择方面的一致性。我们使用改进的 EM 算法结合近似梯度法来实现这些方法，从而在算法的 M 步中方便地进行闭式参数更新。我们通过仿真检验了这些方法的有限样本性能，并在一个探索人体测量关系的真实数据示例中演示了这些方法的应用。
{"title":"Estimation and group-feature selection in sparse mixture-of-experts with diverging number of parameters","authors":"Abbas Khalili , Archer Yi Yang , Xiaonan Da","doi":"10.1016/j.jspi.2024.106250","DOIUrl":"10.1016/j.jspi.2024.106250","url":null,"abstract":"<div><div>Mixture-of-experts provide flexible statistical models for a wide range of regression (supervised learning) problems. Often a large number of covariates (features) are available in many modern applications yet only a small subset of them is useful in explaining a response variable of interest. This calls for a feature selection device. In this paper, we present new group-feature selection and estimation methods for sparse mixture-of-experts models when the number of features can be nearly comparable to the sample size. We prove the consistency of the methods in both parameter estimation and feature selection. We implement the methods using a modified EM algorithm combined with proximal gradient method which results in a convenient closed-form parameter update in the M-step of the algorithm. We examine the finite-sample performance of the methods through simulations, and demonstrate their applications in a real data example on exploring relationships in body measurements.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"237 ","pages":"Article 106250"},"PeriodicalIF":0.8,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705363","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 : 2025-07-01Epub Date: 2024-11-14DOI: 10.1016/j.jspi.2024.106249
Li Xun , Xin Guan , Yong Zhou
Exploring quantile differences between two populations at various probability levels offers valuable insights into their distinctions, which are essential for practical applications such as assessing treatment effects. However, estimating these differences can be challenging due to the complex data often encountered in clinical trials. This paper assumes that right-censored data and length-biased right-censored data originate from two populations of interest. We propose an adjusted smoothed empirical likelihood (EL) method for inferring quantile differences and establish the asymptotic properties of the proposed estimators. Under mild conditions, we demonstrate that the adjusted log-EL ratio statistics asymptotically follow the standard chi-squared distribution. We construct confidence intervals for the quantile differences using both normal and chi-squared approximations and develop a likelihood ratio test for these differences. The performance of our proposed methods is illustrated through simulation studies. Finally, we present a case study utilizing Oscar award nomination data to demonstrate the application of our method.
{"title":"Semi-parametric empirical likelihood inference on quantile difference between two samples with length-biased and right-censored data","authors":"Li Xun , Xin Guan , Yong Zhou","doi":"10.1016/j.jspi.2024.106249","DOIUrl":"10.1016/j.jspi.2024.106249","url":null,"abstract":"<div><div>Exploring quantile differences between two populations at various probability levels offers valuable insights into their distinctions, which are essential for practical applications such as assessing treatment effects. However, estimating these differences can be challenging due to the complex data often encountered in clinical trials. This paper assumes that right-censored data and length-biased right-censored data originate from two populations of interest. We propose an adjusted smoothed empirical likelihood (EL) method for inferring quantile differences and establish the asymptotic properties of the proposed estimators. Under mild conditions, we demonstrate that the adjusted log-EL ratio statistics asymptotically follow the standard chi-squared distribution. We construct confidence intervals for the quantile differences using both normal and chi-squared approximations and develop a likelihood ratio test for these differences. The performance of our proposed methods is illustrated through simulation studies. Finally, we present a case study utilizing Oscar award nomination data to demonstrate the application of our method.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"237 ","pages":"Article 106249"},"PeriodicalIF":0.8,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705362","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 : 2025-07-01Epub Date: 2024-12-04DOI: 10.1016/j.jspi.2024.106253
Jie Yin , Jieli Ding , Changming Yang
In order to break the constraints and barriers caused by limited computing power in processing massive datasets, we propose an outcome dependent subsampling divide and conquer strategy in this paper. The proposed strategy can process data on multiple blocks in parallel and concentrate the computing resources of each block on regions with the most information. We develop a distributed statistical inference method and propose a computation-efficient algorithm in the generalized linear models for massive data. The proposed method only need to preserve some summary statistics from each data block and then use them to directly construct the proposed estimator. The asymptotic properties of the proposed method are established. Simulation studies and real data analysis are conducted to illustrate the merits of the proposed method.
{"title":"Outcome dependent subsampling divide and conquer in generalized linear models for massive data","authors":"Jie Yin , Jieli Ding , Changming Yang","doi":"10.1016/j.jspi.2024.106253","DOIUrl":"10.1016/j.jspi.2024.106253","url":null,"abstract":"<div><div>In order to break the constraints and barriers caused by limited computing power in processing massive datasets, we propose an outcome dependent subsampling divide and conquer strategy in this paper. The proposed strategy can process data on multiple blocks in parallel and concentrate the computing resources of each block on regions with the most information. We develop a distributed statistical inference method and propose a computation-efficient algorithm in the generalized linear models for massive data. The proposed method only need to preserve some summary statistics from each data block and then use them to directly construct the proposed estimator. The asymptotic properties of the proposed method are established. Simulation studies and real data analysis are conducted to illustrate the merits of the proposed method.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"237 ","pages":"Article 106253"},"PeriodicalIF":0.8,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133629","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 : 2025-07-01Epub Date: 2024-12-18DOI: 10.1016/j.jspi.2024.106252
Kazuhiko Hayakawa, Boyan Yin
This paper proposes the maximum likelihood (ML) estimator for a short panel autoregressive model with a flexible form of observed factors as well as unknown interactive fixed effects. We show that the ML estimator is consistent and asymptotically normally distributed as the number of cross-sectional units increases with the number of time periods being fixed. It should be noted that this asymptotic result holds uniformly for the autoregressive coefficient less than, equal to, or greater than one, in sharp contrast to existing estimators. Monte Carlo simulation results show that the ML estimator has desirable finite sample properties.
{"title":"Maximum likelihood estimation of short panel autoregressive models with flexible form of fixed effects","authors":"Kazuhiko Hayakawa, Boyan Yin","doi":"10.1016/j.jspi.2024.106252","DOIUrl":"10.1016/j.jspi.2024.106252","url":null,"abstract":"<div><div>This paper proposes the maximum likelihood (ML) estimator for a short panel autoregressive model with a flexible form of observed factors as well as unknown interactive fixed effects. We show that the ML estimator is consistent and asymptotically normally distributed as the number of cross-sectional units increases with the number of time periods being fixed. It should be noted that this asymptotic result holds uniformly for the autoregressive coefficient less than, equal to, or greater than one, in sharp contrast to existing estimators. Monte Carlo simulation results show that the ML estimator has desirable finite sample properties.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"237 ","pages":"Article 106252"},"PeriodicalIF":0.8,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133630","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 : 2025-07-01Epub Date: 2024-12-30DOI: 10.1016/j.jspi.2024.106261
Bingjing Tang , Vinayak Rao
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. In many situations, an applied scientist may have additional informative beliefs about the data distribution of interest, for instance, the distribution of its mean or a subset components. This often will not be compatible with the nonparametric prior. An important challenge is then to incorporate this partial prior belief into nonparametric Bayesian models. In this paper, we are motivated by settings where practitioners have additional distributional information about a subset of the coordinates of the observations being modeled. Our approach links this problem to that of conditional density modeling. Our main idea is a novel constrained Bayesian model, based on a perturbation of a parametric distribution with a transformed Gaussian process prior on the perturbation function. We develop a corresponding posterior sampling method based on data augmentation. We illustrate the efficacy of our proposed constrained nonparametric Bayesian model in a variety of real-world scenarios including modeling environmental and earthquake data.
{"title":"Marginally constrained nonparametric Bayesian inference through Gaussian processes","authors":"Bingjing Tang , Vinayak Rao","doi":"10.1016/j.jspi.2024.106261","DOIUrl":"10.1016/j.jspi.2024.106261","url":null,"abstract":"<div><div>Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. In many situations, an applied scientist may have additional informative beliefs about the data distribution of interest, for instance, the distribution of its mean or a subset components. This often will not be compatible with the nonparametric prior. An important challenge is then to incorporate this partial prior belief into nonparametric Bayesian models. In this paper, we are motivated by settings where practitioners have additional distributional information about a subset of the coordinates of the observations being modeled. Our approach links this problem to that of conditional density modeling. Our main idea is a novel constrained Bayesian model, based on a perturbation of a parametric distribution with a transformed Gaussian process prior on the perturbation function. We develop a corresponding posterior sampling method based on data augmentation. We illustrate the efficacy of our proposed constrained nonparametric Bayesian model in a variety of real-world scenarios including modeling environmental and earthquake data.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"237 ","pages":"Article 106261"},"PeriodicalIF":0.8,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133631","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 : 2025-07-01Epub Date: 2024-12-28DOI: 10.1016/j.jspi.2024.106262
Liuping Hu , Kashinath Chatterjee , Jianhui Ning , Hong Qin
Asymmetrical (mixed-level) uniform designs are useful for both computer and physical experiments. However, constructing these designs is often challenging due to their complex asymmetrical structure. In this paper, we propose novel methods for constructing uniform designs with mixed two-, three-, and four/nine-levels. Our construction methods are deterministic, allowing us to circumvent the complexity associated with stochastic algorithms. We evaluate uniformity using the wrap-around - and Lee discrepancies. We establish useful analytic relationships between uniformity and aberration, and derive new general lower bounds for discrepancies that are tighter than those currently available in the literature. These new benchmarks can effectively measure the uniformity of asymmetrical designs. Additionally, we provide examples demonstrating the efficacy of our construction methods and the relevance of the newly obtained lower bounds. Finally, through simulations, we show that the designs produced using our methods perform well in constructing statistical surrogate models.
{"title":"Deterministic construction methods for asymmetrical uniform designs","authors":"Liuping Hu , Kashinath Chatterjee , Jianhui Ning , Hong Qin","doi":"10.1016/j.jspi.2024.106262","DOIUrl":"10.1016/j.jspi.2024.106262","url":null,"abstract":"<div><div>Asymmetrical (mixed-level) uniform designs are useful for both computer and physical experiments. However, constructing these designs is often challenging due to their complex asymmetrical structure. In this paper, we propose novel methods for constructing uniform designs with mixed two-, three-, and four/nine-levels. Our construction methods are deterministic, allowing us to circumvent the complexity associated with stochastic algorithms. We evaluate uniformity using the wrap-around <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>- and Lee discrepancies. We establish useful analytic relationships between uniformity and aberration, and derive new general lower bounds for discrepancies that are tighter than those currently available in the literature. These new benchmarks can effectively measure the uniformity of asymmetrical designs. Additionally, we provide examples demonstrating the efficacy of our construction methods and the relevance of the newly obtained lower bounds. Finally, through simulations, we show that the designs produced using our methods perform well in constructing statistical surrogate models.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"237 ","pages":"Article 106262"},"PeriodicalIF":0.8,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143133632","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 : 2025-05-01Epub Date: 2024-10-01DOI: 10.1016/j.jspi.2024.106243
David J. Hessen
In this paper, a family of maximum-entropy distributions with general discrete support is derived. Members of the family are distinguished by the number of specified non-central moments. In addition, a subfamily of discrete symmetric distributions is defined. Attention is paid to maximum likelihood estimation of the parameters of any member of the general family. It is shown that the parameters of any special case with infinite support can be estimated using a conditional distribution given a finite subset of the total support. In an empirical data example, the procedures proposed are demonstrated.
{"title":"A family of discrete maximum-entropy distributions","authors":"David J. Hessen","doi":"10.1016/j.jspi.2024.106243","DOIUrl":"10.1016/j.jspi.2024.106243","url":null,"abstract":"<div><div>In this paper, a family of maximum-entropy distributions with general discrete support is derived. Members of the family are distinguished by the number of specified non-central moments. In addition, a subfamily of discrete symmetric distributions is defined. Attention is paid to maximum likelihood estimation of the parameters of any member of the general family. It is shown that the parameters of any special case with infinite support can be estimated using a conditional distribution given a finite subset of the total support. In an empirical data example, the procedures proposed are demonstrated.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"236 ","pages":"Article 106243"},"PeriodicalIF":0.8,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416588","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}
Pub Date : 2025-05-01Epub Date: 2024-09-04DOI: 10.1016/j.jspi.2024.106230
Rong Yan, Shanqi Pang, Jing Wang, Mengqian Chen
Schematic orthogonal arrays are closely related to association schemes. And which orthogonal arrays are schematic orthogonal arrays and how to classify them is an open problem proposed by Hedayat et al. (1999). By using the Hamming distances, this paper presents some general methods for constructing schematic symmetric and mixed orthogonal arrays of high strength. As applications of these methods, we construct association schemes and many new schematic orthogonal arrays including several infinite classes of such arrays. Some examples are provided to illustrate the construction methods. The paper gives the partial solution of the problem by Hedayat et al. (1999) for symmetric and mixed orthogonal arrays of high strength.
{"title":"On schematic orthogonal arrays of high strength","authors":"Rong Yan, Shanqi Pang, Jing Wang, Mengqian Chen","doi":"10.1016/j.jspi.2024.106230","DOIUrl":"10.1016/j.jspi.2024.106230","url":null,"abstract":"<div><p>Schematic orthogonal arrays are closely related to association schemes. And which orthogonal arrays are schematic orthogonal arrays and how to classify them is an open problem proposed by Hedayat et al. (1999). By using the Hamming distances, this paper presents some general methods for constructing schematic symmetric and mixed orthogonal arrays of high strength. As applications of these methods, we construct association schemes and many new schematic orthogonal arrays including several infinite classes of such arrays. Some examples are provided to illustrate the construction methods. The paper gives the partial solution of the problem by Hedayat et al. (1999) for symmetric and mixed orthogonal arrays of high strength.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"236 ","pages":"Article 106230"},"PeriodicalIF":0.8,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142162837","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 : 2025-05-01Epub Date: 2024-09-03DOI: 10.1016/j.jspi.2024.106229
Becky Tang , Henry A. Frye , John A. Silander Jr. , Alan E. Gelfand
A frequent challenge encountered in real-world applications is data having a high proportion of zeros. Focusing on ecological abundance data, much attention has been given to zero-inflated count data. Models for non-negative continuous abundance data with an excess of zeros are rarely discussed. Work presented here considers the creation of a point mass at zero through a left-censoring approach or through a hurdle approach. We incorporate both mechanisms to capture the analog of zero-inflation for count data. Additionally, primary attention has been given to univariate zero-inflated modeling (e.g., single species), whereas data often arise jointly (e.g., a collection of species). With multivariate abundance data, a key issue is to capture dependence among the species at a site, both in terms of positive abundance as well as absence. Therefore, our contribution is a model for multivariate zero-inflated continuous data that are non-negative. Working in a Bayesian framework, we discuss the issue of separating the two sources of zeros and offer model comparison metrics for multivariate zero-inflated data. In an application, we model the total biomass for five tree species obtained from plots established in the Forest Inventory Analysis database in the Northeast region of the United States.
{"title":"Zero-inflated multivariate tobit regression modeling","authors":"Becky Tang , Henry A. Frye , John A. Silander Jr. , Alan E. Gelfand","doi":"10.1016/j.jspi.2024.106229","DOIUrl":"10.1016/j.jspi.2024.106229","url":null,"abstract":"<div><p>A frequent challenge encountered in real-world applications is data having a high proportion of zeros. Focusing on ecological abundance data, much attention has been given to zero-inflated count data. Models for non-negative continuous abundance data with an excess of zeros are rarely discussed. Work presented here considers the creation of a point mass at zero through a left-censoring approach or through a hurdle approach. We incorporate both mechanisms to capture the analog of zero-inflation for count data. Additionally, primary attention has been given to univariate zero-inflated modeling (e.g., single species), whereas data often arise jointly (e.g., a collection of species). With multivariate abundance data, a key issue is to capture dependence among the species at a site, both in terms of positive abundance as well as absence. Therefore, our contribution is a model for multivariate zero-inflated continuous data that are non-negative. Working in a Bayesian framework, we discuss the issue of separating the two sources of zeros and offer model comparison metrics for multivariate zero-inflated data. In an application, we model the total biomass for five tree species obtained from plots established in the Forest Inventory Analysis database in the Northeast region of the United States.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"236 ","pages":"Article 106229"},"PeriodicalIF":0.8,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142150410","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 : 2025-05-01Epub Date: 2024-08-26DOI: 10.1016/j.jspi.2024.106228
Kwan-Young Bak , Woojoo Lee
Despite the curse of dimensionality, kernel ridge regression often exhibits good performance in practical applications, even when the dimension is moderately large. However, it has been shown that kernel ridge regression cannot be free from the curse of dimensionality. Until now, the literature on kernel ridge regression has suggested that the gap between theory and practice in relation to dimensionality has not narrowed. In this study, we first investigate when the influence of dimensionality does not significantly affect the convergence rate of the kernel ridge regression. Specifically, we study the convergence rate of and risks for the kernel ridge estimator, with a focus on reproducing kernel Hilbert space (RKHS) generated by a product kernel. We show that the univariate optimal convergence rate up to a logarithmic factor in and risks can be achieved by controlling the size of the RKHS. The result of a numerical study confirms our theoretical findings.
{"title":"Effect of dimensionality on convergence rates of kernel ridge regression estimator","authors":"Kwan-Young Bak , Woojoo Lee","doi":"10.1016/j.jspi.2024.106228","DOIUrl":"10.1016/j.jspi.2024.106228","url":null,"abstract":"<div><div>Despite the curse of dimensionality, kernel ridge regression often exhibits good performance in practical applications, even when the dimension is moderately large. However, it has been shown that kernel ridge regression cannot be free from the curse of dimensionality. Until now, the literature on kernel ridge regression has suggested that the gap between theory and practice in relation to dimensionality has not narrowed. In this study, we first investigate when the influence of dimensionality does not significantly affect the convergence rate of the kernel ridge regression. Specifically, we study the convergence rate of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> risks for the kernel ridge estimator, with a focus on reproducing kernel Hilbert space (RKHS) generated by a product kernel. We show that the univariate optimal convergence rate up to a logarithmic factor in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> risks can be achieved by controlling the size of the RKHS. The result of a numerical study confirms our theoretical findings.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"236 ","pages":"Article 106228"},"PeriodicalIF":0.8,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180125","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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