Electronic Journal of Statistics最新文献_第10页

Dimension independent excess risk by stochastic gradient descent 随机梯度下降的维数无关超额风险

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2055

X. Chen, Qiang Liu, Xin T. Tong

引用次数: 2

Penalized estimation of threshold auto-regressive models with many components and thresholds. 多成分多阈值阈值自回归模型的惩罚性估计

IF 1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 Epub Date: 2022-03-22 DOI: 10.1214/22-EJS1982

Kunhui Zhang, Abolfazl Safikhani, Alex Tank, Ali Shojaie

{"title":"Penalized estimation of threshold auto-regressive models with many components and thresholds.","authors":"Kunhui Zhang, Abolfazl Safikhani, Alex Tank, Ali Shojaie","doi":"10.1214/22-EJS1982","DOIUrl":"10.1214/22-EJS1982","url":null,"abstract":"<p><p>Thanks to their simplicity and interpretable structure, autoregressive processes are widely used to model time series data. However, many real time series data sets exhibit non-linear patterns, requiring nonlinear modeling. The threshold Auto-Regressive (TAR) process provides a family of non-linear auto-regressive time series models in which the process dynamics are specific step functions of a thresholding variable. While estimation and inference for low-dimensional TAR models have been investigated, high-dimensional TAR models have received less attention. In this article, we develop a new framework for estimating high-dimensional TAR models, and propose two different sparsity-inducing penalties. The first penalty corresponds to a natural extension of classical TAR model to high-dimensional settings, where the same threshold is enforced for all model parameters. Our second penalty develops a more flexible TAR model, where different thresholds are allowed for different auto-regressive coefficients. We show that both penalized estimation strategies can be utilized in a three-step procedure that consistently learns both the thresholds and the corresponding auto-regressive coefficients. However, our theoretical and empirical investigations show that the direct extension of the TAR model is not appropriate for high-dimensional settings and is better suited for moderate dimensions. In contrast, the more flexible extension of the TAR model leads to consistent estimation and superior empirical performance in high dimensions.</p>","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"16 1","pages":"1891-1951"},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10088520/pdf/nihms-1885625.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9851486","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

On sufficient variable screening using log odds ratio filter 利用对数比值比滤波器进行充分变量筛选

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/21-ejs1951

Baoying Yang, Wenbo Wu, Xiangrong Yin

引用次数: 0

Monte Carlo Markov chains constrained on graphs for a target with disconnected support 具有断开支持的目标在图上约束的蒙特卡罗马尔可夫链

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2043

R. Cerqueti, Emilio De Santis

引用次数: 0

The robust nearest shrunken centroids classifier for high-dimensional heavy-tailed data 高维重尾数据的鲁棒最近收缩质心分类器

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2022

Shaokang Ren, Qing Mai

引用次数: 0

Two-sample test for equal distributions in separate metric space: New maximum mean discrepancy based approaches 独立度量空间中相等分布的两样本检验：基于最大均值差异的新方法

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2033

Jin-Ting Zhang, Łukasz Smaga

引用次数: 1

Functional estimation of anisotropic covariance and autocovariance operators on the sphere 球面上各向异性协方差和自协方差算子的函数估计

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2021-12-23 DOI: 10.1214/22-ejs2064

Alessia Caponera, J. Fageot, Matthieu Simeoni, V. Panaretos

{"title":"Functional estimation of anisotropic covariance and autocovariance operators on the sphere","authors":"Alessia Caponera, J. Fageot, Matthieu Simeoni, V. Panaretos","doi":"10.1214/22-ejs2064","DOIUrl":"https://doi.org/10.1214/22-ejs2064","url":null,"abstract":"We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distributed collection of spherical random fields is sampled at a few random directions, possibly subject to measurement error. The collection of random fields could be i.i.d. or serially dependent. Though similar setups have already been explored for random functions defined on the unit interval, the nonparametric estimators proposed in the literature often rely on local polynomials, which do not readily extend to the (product) spherical setting. We therefore formulate our estimation procedure as a variational problem involving a generalized Tikhonov regularization term. The latter favours smooth covariance/autocovariance functions, where the smoothness is specified by means of suitable Sobolev-like pseudo-differential operators. Using the machinery of reproducing kernel Hilbert spaces, we establish representer theorems that fully characterize the form of our estimators. We determine their uniform rates of convergence as the number of random fields diverges, both for the dense (increasing number of spatial samples) and sparse (bounded number of spatial samples) regimes. We moreover demonstrate the computational feasibility and practical merits of our estimation procedure in a simulation setting, assuming a fixed number of samples per random field. Our numerical estimation procedure leverages the sparsity and second-order Kronecker structure of our setup to reduce the computational and memory requirements by approximately three orders of magnitude compared to a naive implementation would require. AMS 2000 subject classifications: Primary 62G08; secondary 62M.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49616151","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

Convergence properties of data augmentation algorithms for high-dimensional robit regression 高维robit回归数据增广算法的收敛性

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2021-12-20 DOI: 10.1214/22-ejs2098

Sourav Mukherjee, K. Khare, Saptarshi Chakraborty Department of Statistics, U. Florida, D. Biostatistics, State University of New York at Buffalo

{"title":"Convergence properties of data augmentation algorithms for high-dimensional robit regression","authors":"Sourav Mukherjee, K. Khare, Saptarshi Chakraborty Department of Statistics, U. Florida, D. Biostatistics, State University of New York at Buffalo","doi":"10.1214/22-ejs2098","DOIUrl":"https://doi.org/10.1214/22-ejs2098","url":null,"abstract":"Abstract: The logistic and probit link functions are the most common choices for regression models with a binary response. However, these choices are not robust to the presence of outliers/unexpected observations. The robit link function, which is equal to the inverse CDF of the Student’s t-distribution, provides a robust alternative to the probit and logistic link functions. A multivariate normal prior for the regression coefficients is the standard choice for Bayesian inference in robit regression models. The resulting posterior density is intractable and a Data Augmentation (DA) Markov chain is used to generate approximate samples from the desired posterior distribution. Establishing geometric ergodicity for this DA Markov chain is important as it provides theoretical guarantees for asymptotic validity of MCMC standard errors for desired posterior expectations/quantiles. Previous work [1] established geometric ergodicity of this robit DA Markov chain assuming (i) the sample size n dominates the number of predictors p, and (ii) an additional constraint which requires the sample size to be bounded above by a fixed constant which depends on the design matrix X. In particular, modern highdimensional settings where n < p are not considered. In this work, we show that the robit DA Markov chain is trace-class (i.e., the eigenvalues of the corresponding Markov operator are summable) for arbitrary choices of the sample size n, the number of predictors p, the design matrix X, and the prior mean and variance parameters. The trace-class property implies geometric ergodicity. Moreover, this property allows us to conclude that the sandwich robit chain (obtained by inserting an inexpensive extra step in between the two steps of the DA chain) is strictly better than the robit DA chain in an appropriate sense, and enables the use of recent methods to estimate the spectral gap of trace class DA Markov chains.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48632525","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

Flexible inference of optimal individualized treatment strategy in covariate adjusted randomization with multiple covariates 多协变量调整随机化中最优个体化治疗策略的灵活推断

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2021-11-19 DOI: 10.1214/23-ejs2127

Trinetri Ghosh, Yanyuan Ma, Rui Song, Pingshou Zhong

引用次数: 0

Bounds in L1 Wasserstein distance on the normal approximation of general M-estimators 一般m估计量的正态逼近在L1 Wasserstein距离上的界

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2021-11-18 DOI: 10.1214/23-ejs2132

F. Bachoc, M. Fathi

引用次数: 0