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High-dimensional composite quantile regression: Optimal statistical guarantees and fast algorithms 高维复合分位数回归:最优统计保证和快速算法
4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2147
Haeseong Moon, Wen-Xin Zhou
{"title":"High-dimensional composite quantile regression: Optimal statistical guarantees and fast algorithms","authors":"Haeseong Moon, Wen-Xin Zhou","doi":"10.1214/23-ejs2147","DOIUrl":"https://doi.org/10.1214/23-ejs2147","url":null,"abstract":"The composite quantile regression (CQR) was introduced by Zou and Yuan [Ann. Statist. 36 (2008) 1108–1126] as a robust regression method for linear models with heavy-tailed errors while achieving high efficiency. Its penalized counterpart for high-dimensional sparse models was recently studied in Gu and Zou [IEEE Trans. Inf. Theory 66 (2020) 7132–7154], along with a specialized optimization algorithm based on the alternating direct method of multipliers (ADMM). Compared to the various first-order algorithms for penalized least squares, ADMM-based algorithms are not well-adapted to large-scale problems. To overcome this computational hardness, in this paper we employ a convolution-smoothed technique to CQR, complemented with iteratively reweighted ℓ1-regularization. The smoothed composite loss function is convex, twice continuously differentiable, and locally strong convex with high probability. We propose a gradient-based algorithm for penalized smoothed CQR via a variant of the majorize-minimization principal, which gains substantial computational efficiency over ADMM. Theoretically, we show that the iteratively reweighted ℓ1-penalized smoothed CQR estimator achieves near-minimax optimal convergence rate under heavy-tailed errors without any moment constraint, and further achieves near-oracle convergence rate under a weaker minimum signal strength condition than needed in Gu and Zou (2020). Numerical studies demonstrate that the proposed method exhibits significant computational advantages without compromising statistical performance compared to two state-of-the-art methods that achieve robustness and high efficiency simultaneously.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"38 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":"135911568","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: 1
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
Estimating causal effects with hidden confounding using instrumental variables and environments 使用工具变量和环境估计隐含混淆的因果效应
4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2160
James P. Long, Hongxu Zhu, Kim-Anh Do, Min Jin Ha
{"title":"Estimating causal effects with hidden confounding using instrumental variables and environments","authors":"James P. Long, Hongxu Zhu, Kim-Anh Do, Min Jin Ha","doi":"10.1214/23-ejs2160","DOIUrl":"https://doi.org/10.1214/23-ejs2160","url":null,"abstract":"Recent works have proposed regression models which are invariant across data collection environments [24, 20, 11, 16, 8]. These estimators often have a causal interpretation under conditions on the environments and type of invariance imposed. One recent example, the Causal Dantzig (CD), is consistent under hidden confounding and represents an alternative to classical instrumental variable estimators such as Two Stage Least Squares (TSLS). In this work we derive the CD as a generalized method of moments (GMM) estimator. The GMM representation leads to several practical results, including 1) creation of the Generalized Causal Dantzig (GCD) estimator which can be applied to problems with continuous environments where the CD cannot be fit 2) a Hybrid (GCD-TSLS combination) estimator which has properties superior to GCD or TSLS alone 3) straightforward asymptotic results for all methods using GMM theory. We compare the CD, GCD, TSLS, and Hybrid estimators in simulations and an application to a Flow Cytometry data set. The newly proposed GCD and Hybrid estimators have superior performance to existing methods in many settings.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"4 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":"135610266","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
Asymptotic analysis of ML-covariance parameter estimators based on covariance approximations 基于协方差近似的ml -协方差参数估计的渐近分析
4区 数学
Electronic Journal of Statistics Pub Date : 2023-01-01 DOI: 10.1214/23-ejs2170
Reinhard Furrer, Michael Hediger
{"title":"Asymptotic analysis of ML-covariance parameter estimators based on covariance approximations","authors":"Reinhard Furrer, Michael Hediger","doi":"10.1214/23-ejs2170","DOIUrl":"https://doi.org/10.1214/23-ejs2170","url":null,"abstract":"Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions. Truncated-likelihood functions are based on direct functional approximations of the presumed family of covariance functions. For compactly supported covariance functions, within an increasing-domain asymptotic framework, we provide sufficient conditions under which consistency and asymptotic normality of estimators based on truncated-likelihood functions are preserved. We apply our result to the family of generalized Wendland covariance functions and discuss several examples of Wendland approximations. For families of covariance functions that are not compactly supported, we combine our results with the covariance tapering approach and show that ML estimators, based on truncated-tapered likelihood functions, asymptotically minimize the Kullback-Leibler divergence, when the taper range is fixed.","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":"135662412","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
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
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
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
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