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Efficient sampling from the PKBD distribution 从PKBD分布中有效采样
4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2149
Lukas Sablica, Kurt Hornik, Josef Leydold
{"title":"Efficient sampling from the PKBD distribution","authors":"Lukas Sablica, Kurt Hornik, Josef Leydold","doi":"10.1214/23-ejs2149","DOIUrl":"https://doi.org/10.1214/23-ejs2149","url":null,"abstract":"In this paper we present and analyze random number generators for the Poisson Kernel-Based Distribution (PKBD) on the sphere. We show that the only currently available sampling scheme presented in Golzy and Markatou (2020) can be improved by a better selection of hyper-parameters but still yields an unbounded rejection constant as the concentration parameter approaches 1. Furthermore, we introduce two additional and superior sampling methods for which boundedness in the above mentioned case can be obtained. The first method proposes initial draws from angular central Gaussian distribution and offers uniformly bounded rejection constants for a significant part of the PKBD parameter space. The second method uses adaptive rejection sampling and the results of Ulrich (1984) to sample from the projected Saw distribution (Saw, 1978). Finally, both new methods are compared in a simulation study.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"1 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":"135911577","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
Covariance discriminative power of kernel clustering methods 核聚类方法的协方差判别能力
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2107
A. Kammoun, Romain Couillet
{"title":"Covariance discriminative power of kernel clustering methods","authors":"A. Kammoun, Romain Couillet","doi":"10.1214/23-ejs2107","DOIUrl":"https://doi.org/10.1214/23-ejs2107","url":null,"abstract":"","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":"48173445","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
Efficient density estimation in an AR(1) model AR(1)模型的有效密度估计
4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2166
Anton Schick, Wolfgang Wefelmeyer
{"title":"Efficient density estimation in an AR(1) model","authors":"Anton Schick, Wolfgang Wefelmeyer","doi":"10.1214/23-ejs2166","DOIUrl":"https://doi.org/10.1214/23-ejs2166","url":null,"abstract":"This paper studies a class of plug-in estimators of the stationary density of an autoregressive model with autoregression parameter 0<ϱ<1. These use two types of estimator of the innovation density, a standard kernel estimator and a weighted kernel estimator with weights chosen to mimic the condition that the innovation density has mean zero. Bahadur expansions are obtained for this class of estimators in L1, the space of integrable functions. These stochastic expansions establish root-n consistency in the L1-norm. It is shown that the density estimators based on the weighted kernel estimators are asymptotically efficient if an asymptotically efficient estimator of the autoregression parameter is used. Here asymptotic efficiency is understood in the sense of the Hájek–Le Cam convolution theorem.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"358 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":"135610486","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
Least sum of squares of trimmed residuals regression 裁剪残差回归的最小平方和
4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2164
Yijun Zuo, Hanwen Zuo
{"title":"Least sum of squares of trimmed residuals regression","authors":"Yijun Zuo, Hanwen Zuo","doi":"10.1214/23-ejs2164","DOIUrl":"https://doi.org/10.1214/23-ejs2164","url":null,"abstract":"In the famous least sum of trimmed squares (LTS) estimator [21], residuals are first squared and then trimmed. In this article, we first trim residuals – using a depth trimming scheme – and then square the remaining of residuals. The estimator that minimizes the sum of trimmed and squared residuals, is called an LST estimator. Not only is the LST a robust alternative to the classic least sum of squares (LS) estimator. It also has a high finite sample breakdown point-and can resist, asymptotically, up to 50% contamination without breakdown – in sharp contrast to the 0% of the LS estimator. The population version of the LST is Fisher consistent, and the sample version is strong, root-n consistent, and asymptotically normal. We propose approximate algorithms for computing the LST and test on synthetic and real data sets. Despite being approximate, one of the algorithms compute the LST estimator quickly with relatively small variances in contrast to the famous LTS estimator. Thus, evidence suggests the LST serves as a robust alternative to the LS estimator and is feasible even in high dimension data sets with contamination and outliers.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"2010 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":"136202186","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: 5
Corrigendum to “Maximum likelihood estimation in logistic regression models with a diverging number of covariates” 更正“具有发散协变量数的逻辑回归模型中的最大似然估计”
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/12-EJS731
Hua Liang, Pang Du
{"title":"Corrigendum to “Maximum likelihood estimation in logistic regression models with a diverging number of covariates”","authors":"Hua Liang, Pang Du","doi":"10.1214/12-EJS731","DOIUrl":"https://doi.org/10.1214/12-EJS731","url":null,"abstract":"Binary data with high-dimensional covariates have become more and more common in many disciplines. In this paper we consider the maximum likelihood estimation for logistic regression models with a diverging number of covariates. Under mild conditions we establish the asymptotic normality of the maximum likelihood estimate when the number of covariates p goes to infinity with the sample size n in the order of p = o(n). This remarkably improves the existing results that can only allow p growing in an order of o(nα) with α ∈ [1/5, 1/2] [12, 14]. A major innovation in our proof is the use of the injective function. AMS 2000 subject classifications: Primary 62F12; secondary 62J12.","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":"https://sci-hub-pdf.com/10.1214/12-EJS731","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48042414","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: 14
Sieve estimation of semiparametric accelerated mean models with panel count data 具有面板计数数据的半参数加速平均模型的筛估计
IF 1.1 4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2128
Xiangbin Hu, Wen Su, Xingqiu Zhao
{"title":"Sieve estimation of semiparametric accelerated mean models with panel count data","authors":"Xiangbin Hu, Wen Su, Xingqiu Zhao","doi":"10.1214/23-ejs2128","DOIUrl":"https://doi.org/10.1214/23-ejs2128","url":null,"abstract":"","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":"45925239","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
Nonregular designs from Paley’s Hadamard matrices: Generalized resolution, projectivity and hidden projection property 来自Paley Hadamard矩阵的不规则设计:广义分辨率、投影性和隐投影性质
4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2148
Guanzhou Chen, Chenlu Shi, Boxin Tang
{"title":"Nonregular designs from Paley’s Hadamard matrices: Generalized resolution, projectivity and hidden projection property","authors":"Guanzhou Chen, Chenlu Shi, Boxin Tang","doi":"10.1214/23-ejs2148","DOIUrl":"https://doi.org/10.1214/23-ejs2148","url":null,"abstract":"Nonregular designs are attractive, as compared with regular designs, not just because they have flexible run sizes but also because of their performances in terms of generalized resolution, projectivity, and hidden projection property. In this paper, we conduct a comprehensive study on three classes of designs that are obtained from Paley’s two constructions of Hadamard matrices. In terms of generalized resolution, we complete the study of Shi and Tang [15] on strength-two designs by adding results on strength-three designs. In terms of projectivty and hidden projection property, our results substantially expand those of Bulutoglu and Cheng [2]. For the purpose of practical applications, we conduct an extensive search of minimum G-aberration designs from those with maximum generalized resolutions and results are obtained for strength-two designs with 36, 44, 48, 52, 60, 64, 96 and 128 runs and strength-three designs with 72, 88 and 120 runs.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"6 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":"135911387","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
Uncertainty quantification for sparse spectral variational approximations in Gaussian process regression 高斯过程回归中稀疏谱变分近似的不确定性量化
4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2155
Dennis Nieman, Botond Szabo, Harry van Zanten
{"title":"Uncertainty quantification for sparse spectral variational approximations in Gaussian process regression","authors":"Dennis Nieman, Botond Szabo, Harry van Zanten","doi":"10.1214/23-ejs2155","DOIUrl":"https://doi.org/10.1214/23-ejs2155","url":null,"abstract":"We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and limitations for the frequentist coverage of the resulting variational credible sets. We also derive sufficient and necessary lower bounds for the number of inducing variables required to achieve minimax posterior contraction rates. The implications of these results are demonstrated for different choices of priors. In a numerical analysis we consider a wider range of inducing variable methods and observe similar phenomena beyond the scope of our theoretical findings.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"14 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":"135952877","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
Regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates with varying-coefficient models 混合稀疏同步与异步纵向协变量的变系数模型回归分析
4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2175
Congmin Liu, Zhuowei Sun, Hongyuan Cao
{"title":"Regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates with varying-coefficient models","authors":"Congmin Liu, Zhuowei Sun, Hongyuan Cao","doi":"10.1214/23-ejs2175","DOIUrl":"https://doi.org/10.1214/23-ejs2175","url":null,"abstract":"We consider varying-coefficient models for mixed synchronous and asynchronous longitudinal covariates, where asynchronicity refers to the misalignment of longitudinal measurement times within an individual. We propose three different methods of parameter estimation and inference. The first method is a one-step approach that estimates non-parametric regression functions for synchronous and asynchronous longitudinal covariates simultaneously. The second method is a two-step approach in which synchronous longitudinal covariates are regressed with the longitudinal response by centering the synchronous longitudinal covariates first and, in the second step, the residuals from the first step are regressed with asynchronous longitudinal covariates. The third method is the same as the second method except that in the first step, we omit the asynchronous longitudinal covariate and include a non-parametric intercept in the regression analysis of synchronous longitudinal covariates and the longitudinal response. We further construct simultaneous confidence bands for the non-parametric regression functions to quantify the overall magnitude of variation. Extensive simulation studies provide numerical support for the theoretical findings. The practical utility of the methods is illustrated on a dataset from the ADNI study.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"12 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":"135662402","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
Towards optimal doubly robust estimation of heterogeneous causal effects 对异质性因果效应的最优双稳健估计
4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2157
Edward H. Kennedy
{"title":"Towards optimal doubly robust estimation of heterogeneous causal effects","authors":"Edward H. Kennedy","doi":"10.1214/23-ejs2157","DOIUrl":"https://doi.org/10.1214/23-ejs2157","url":null,"abstract":"Heterogeneous effect estimation is crucial in causal inference, with applications across medicine and social science. Many methods for estimating conditional average treatment effects (CATEs) have been proposed, but there are gaps in understanding if and when such methods are optimal. This is especially true when the CATE has nontrivial structure (e.g., smoothness or sparsity). Our work contributes in several ways. First, we study a two-stage doubly robust CATE estimator and give a generic error bound, which yields rates faster than much of the literature. We apply the bound to derive error rates in smooth nonparametric models, and give sufficient conditions for oracle efficiency. Along the way we give a general error bound for regression with estimated outcomes; this is the second main contribution. The third contribution is aimed at understanding the fundamental statistical limits of CATE estimation. To that end, we propose and study a local polynomial adaptation of double-residual regression. We show that this estimator can be oracle efficient under even weaker conditions, and we conjecture that they are minimal in a minimax sense. We go on to give error bounds in the non-trivial regime where oracle rates cannot be achieved. Some finite-sample properties are explored with simulations.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"20 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":"135662404","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: 194
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