Electronic Journal of Statistics最新文献

Direct Bayesian linear regression for distribution-valued covariates. 分布值协变量的直接贝叶斯线性回归。

IF 1 4区数学

Electronic Journal of Statistics Pub Date : 2024-01-01 Epub Date: 2024-08-27 DOI: 10.1214/24-ejs2275

Bohao Tang, Sandipan Pramanik, Yi Zhao, Brian Caffo, Abhirup Datta

{"title":"Direct Bayesian linear regression for distribution-valued covariates.","authors":"Bohao Tang, Sandipan Pramanik, Yi Zhao, Brian Caffo, Abhirup Datta","doi":"10.1214/24-ejs2275","DOIUrl":"10.1214/24-ejs2275","url":null,"abstract":"<p><p>In this manuscript, we study scalar-on-distribution regression; that is, instances where subject-specific distributions or densities are the covariates, related to a scalar outcome via a regression model. In practice, only repeated measures are observed from those covariate distributions and common approaches first use these to estimate subject-specific density functions, which are then used as covariates in standard scalar-on-function regression. We propose a simple and direct method for linear scalar-on-distribution regression that circumvents the intermediate step of estimating subject-specific covariate densities. We show that one can directly use the observed repeated measures as covariates and endow the regression function with a Gaussian process prior to obtain a closed form or conjugate Bayesian inference. Our method subsumes the standard Bayesian non-parametric regression using Gaussian processes as a special case, corresponding to covariates being Dirac-distributions. The model is also invariant to any transformation or ordering of the repeated measures. Theoretically, we show that, despite only using the observed repeated measures from the true density-valued covariates that generated the data, the method can achieve an optimal estimation error bound of the regression function. The theory extends beyond i.i.d. settings to accommodate certain forms of within-subject dependence among the repeated measures. To our knowledge, this is the first theoretical study on Bayesian regression using distribution-valued covariates. We propose numerous extensions including a scalable implementation using low-rank Gaussian processes and a generalization to non-linear scalar-on-distribution regression. Through simulation studies, we demonstrate that our method performs substantially better than approaches that require an intermediate density estimation step especially with a small number of repeated measures per subject. We apply our method to study association of age with activity counts.</p>","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"18 2","pages":"3327-3375"},"PeriodicalIF":1.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11466299/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142401736","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}

引用次数: 0

Should we estimate a product of density functions by a product of estimators? 我们应该用估计量的乘积来估计密度函数的乘积吗？

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2103

F. Comte, C. Duval

引用次数: 0

Statistical inference via conditional Bayesian posteriors in high-dimensional linear regression 基于条件贝叶斯后验的高维线性回归统计推断

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2113

Teng Wu, Naveen N. Narisetty, Yun Yang

引用次数: 2

Subnetwork estimation for spatial autoregressive models in large-scale networks 大规模网络中空间自回归模型的子网络估计

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2139

Xuetong Li, Feifei Wang, Wei Lan, Hansheng Wang

{"title":"Subnetwork estimation for spatial autoregressive models in large-scale networks","authors":"Xuetong Li, Feifei Wang, Wei Lan, Hansheng Wang","doi":"10.1214/23-ejs2139","DOIUrl":"https://doi.org/10.1214/23-ejs2139","url":null,"abstract":"Large-scale networks are commonly encountered in practice (e.g., Facebook and Twitter) by researchers. In order to study the network interaction between different nodes of large-scale networks, the spatial autoregressive (SAR) model has been popularly employed. Despite its popularity, the estimation of a SAR model on large-scale networks remains very challenging. On the one hand, due to policy limitations or high collection costs, it is often impossible for independent researchers to observe or collect all network information. On the other hand, even if the entire network is accessible, estimating the SAR model using the quasi-maximum likelihood estimator (QMLE) could be computationally infeasible due to its high computational cost. To address these challenges, we propose here a subnetwork estimation method based on QMLE for the SAR model. By using appropriate sampling methods, a subnetwork, consisting of a much-reduced number of nodes, can be constructed. Subsequently, the standard QMLE can be computed by treating the sampled subnetwork as if it were the entire network. This leads to a significant reduction in information collection and model computation costs, which increases the practical feasibility of the effort. Theoretically, we show that the subnetwork-based QMLE is consistent and asymptotically normal under appropriate regularity conditions. Extensive simulation studies, based on both simulated and real network structures, are presented.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42334033","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}

引用次数: 0

Variable selection for single-index varying-coefficients models with applications to synergistic G × E interactions 单指标变系数模型的变量选择及其在协同G×E相互作用中的应用

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2117

Shunjie Guan, Mingtao Zhao, Yuehua Cui

引用次数: 0

Bootstrap adjusted predictive classification for identification of subgroups with differential treatment effects under generalized linear models Bootstrap校正预测分类用于识别广义线性模型下具有差异治疗效果的亚组

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2108

Na Li, Yanglei Song, C. D. Lin, D. Tu

引用次数: 0

On nonparametric estimation for cross-sectional sampled data under stationarity 平稳性下截面抽样数据的非参数估计

4区数学

Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2163

Kwun Chuen Gary Chan, Hok Kan Ling, Sheung Chi Phillip Yam

引用次数: 0

Envelopes and principal component regression 包络和主成分回归

4区数学

Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2154

Xin Zhang, Kai Deng, Qing Mai

{"title":"Envelopes and principal component regression","authors":"Xin Zhang, Kai Deng, Qing Mai","doi":"10.1214/23-ejs2154","DOIUrl":"https://doi.org/10.1214/23-ejs2154","url":null,"abstract":"Envelope methods offer targeted dimension reduction for various statistical models. The goal is to improve efficiency in multivariate parameter estimation by projecting the data onto a lower-dimensional subspace known as the envelope. Envelope approaches have advantages in analyzing data with highly correlated variables, but their iterative Grassmannian optimization algorithms do not scale very well with high-dimensional data. While the connections between envelopes and partial least squares in multivariate linear regression have promoted recent progress in high-dimensional studies of envelopes, we propose a more straightforward way of envelope modeling from a new principal component regression perspective. The proposed procedure, Non-Iterative Envelope Component Estimation (NIECE), has excellent computational advantages over the iterative Grassmannian optimization alternatives in high dimensions. We develop a unified theory that bridges the gap between envelope methods and principal components in regression. The new theoretical insights also shed light on the envelope subspace estimation error as a function of eigenvalue gaps of two symmetric positive definite matrices used in envelope modeling. We apply the new theory and algorithm to several envelope models, including response and predictor reduction in multivariate linear models, logistic regression, and Cox proportional hazard model. Simulations and illustrative data analysis show the potential for NIECE to improve standard methods in linear and generalized linear models significantly.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136207137","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}

引用次数: 2

Characterization of the solutions set of the generalized LASSO problems for non-full rank cases 非满秩情况下广义LASSO问题解集的刻画

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2138

Jaesung Hwang, Joong-Yeon Won, Yongdai Kim

引用次数: 0

Tests for high-dimensional single-index models 高维单索引模型的测试

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2109

Leheng Cai, Xu Guo, Gaorong Li, Falong Tan

引用次数: 1