Electronic Journal of Statistics最新文献_第8页

Adaptive threshold-based classification of sparse high-dimensional data 基于自适应阈值的稀疏高维数据分类

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs1998

T. Pavlenko, N. Stepanova, Lee Thompson

{"title":"Adaptive threshold-based classification of sparse high-dimensional data","authors":"T. Pavlenko, N. Stepanova, Lee Thompson","doi":"10.1214/22-ejs1998","DOIUrl":"https://doi.org/10.1214/22-ejs1998","url":null,"abstract":"Abstract: We revisit the problem of designing an efficient binary classifier in a challenging high-dimensional framework. The model under study assumes some local dependence structure among feature variables represented by a block-diagonal covariance matrix with a growing number of blocks of an arbitrary, but fixed size. The blocks correspond to non-overlapping independent groups of strongly correlated features. To assess the relevance of a particular block in predicting the response, we introduce a measure of “signal strength” pertaining to each feature block. This measure is then used to specify a sparse model of our interest. We further propose a threshold-based feature selector which operates as a screen-and-clean scheme integrated into a linear classifier: the data is subject to screening and hard threshold cleaning to filter out the blocks that contain no signals. Asymptotic properties of the proposed classifiers are studied when the sample size n depends on the number of feature blocks b, and the sample size goes to infinity with b at a slower rate than b. The new classifiers, which are fully adaptive to unknown parameters of the model, are shown to perform asymptotically optimally in a large part of the classification region. The numerical study confirms good analytical properties of the new classifiers that compare favorably to the existing threshold-based procedure used in a similar context.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47611113","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

Optimal estimation of the supremum and occupation times of a self-similar Lévy process 自相似Lévy过程的上确界和占用时间的最优估计

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/21-ejs1928

J. Ivanovs, M. Podolskij

引用次数: 3

Minimal σ-field for flexible sufficient dimension reduction 最小的σ-域为灵活的充分降维

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs1999

Hanmin Guo, Lin Hou, Y. Zhu

{"title":"Minimal σ-field for flexible sufficient dimension reduction","authors":"Hanmin Guo, Lin Hou, Y. Zhu","doi":"10.1214/22-ejs1999","DOIUrl":"https://doi.org/10.1214/22-ejs1999","url":null,"abstract":"Sufficient Dimension Reduction (SDR) becomes an important tool for mitigating the curse of dimensionality in high dimensional regression analysis. Recently, Flexible SDR (FSDR) has been proposed to extend SDR by finding lower dimensional projections of transformed explanatory variables. The dimensions of the projections however cannot fully represent the extent of data reduction FSDR can achieve. As a consequence, optimality and other theoretical properties of FSDR are currently not well understood. In this article, we propose to use the σ-field associated with the projections, together with their dimensions to fully characterize FSDR, and refer to the σ-field as the FSDR σ-field. We further introduce the concept of minimal FSDR σ-field and consider FSDR projections with the minimal σfield optimal. Under some mild conditions, we show that the minimal FSDR σ-field exists, attaining the lowest dimensionality at the same time. To estimate the minimal FSDR σ-field, we propose a two-stage procedure called the Generalized Kernel Dimension Reduction (GKDR) method and partially establish its consistency property under weak conditions. Extensive simulation experiments demonstrate that the GKDRmethod can effectively find the minimal FSDR σ-field and outperform other existing methods. The application of GKDR to a real life air pollution data set sheds new light on the connections between atmospheric conditions and air quality. MSC2020 subject classifications: Primary 62B05; secondary 62J02.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46459761","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

Estimation of partially conditional average treatment effect by double kernel-covariate balancing 用双核协变量平衡估计部分条件平均治疗效果

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2000

Jiayi Wang, R. K. Wong, Shu Yang, K. C. G. Chan

引用次数: 3

Isotonic regression for elicitable functionals and their Bayes risk 可引出泛函的同调回归及其Bayes风险

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2034

Anja Mühlemann, Johanna F. Ziegel

引用次数: 0

Regularized high dimension low tubal-rank tensor regression 正则化高维低管阶张量回归

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2004

S. Roy, G. Michailidis

{"title":"Regularized high dimension low tubal-rank tensor regression","authors":"S. Roy, G. Michailidis","doi":"10.1214/22-ejs2004","DOIUrl":"https://doi.org/10.1214/22-ejs2004","url":null,"abstract":": Tensor regression models are of emerging interest in diverse ﬁelds of social and behavioral sciences, including neuroimaging analysis, neural networks, image processing and so on. Recent theoretical advance- ments of tensor decomposition have facilitated signiﬁcant development of various tensor regression models. The focus of most of the available lit- erature has been on the Canonical Polyadic (CP) decomposition and its variants for the regression coeﬃcient tensor. A CP decomposed coeﬃcient tensor enables estimation with relatively small sample size, but it may not always capture the underlying complex structure in the data. In this work, we leverage the recently developed concept of tubal rank and develop a tensor regression model, wherein the coeﬃcient tensor is decomposed into two components: a low tubal rank tensor and a structured sparse one. We ﬁrst address the issue of identiﬁability of the two components comprising the coeﬃcient tensor and subsequently develop a fast and scalable Alternating Minimization algorithm to solve the convex regularized program. Further, we provide ﬁnite sample error bounds under high dimensional scaling for the model parameters. The performance of the model is assessed on synthetic data and is also used in an application involving data from an intelligent tutoring platform.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46715850","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

LAMN property for multivariate inhomogeneous diffusions with discrete observations 离散观测下多元非齐次扩散的LAMN性质

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2049

N. Tran, H. Ngo

引用次数: 0

Testing subspace restrictions in the presence of high dimensional nuisance parameters 在存在高维干扰参数的情况下测试子空间限制

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs2058

Alessio Sancetta

引用次数: 0

Concentration inequalities for non-causal random fields 非因果随机场的集中不等式

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs1992

Rémy Garnier, Raphael Langhendries

引用次数: 4

Estimation of the variance matrix in bivariate classical measurement error models 二元经典测量误差模型中方差矩阵的估计

IF 1.1 4区数学

Electronic Journal of Statistics Pub Date : 2022-01-01 DOI: 10.1214/22-ejs1996

Elif Kekeç, I. Van Keilegom

{"title":"Estimation of the variance matrix in bivariate classical measurement error models","authors":"Elif Kekeç, I. Van Keilegom","doi":"10.1214/22-ejs1996","DOIUrl":"https://doi.org/10.1214/22-ejs1996","url":null,"abstract":": The presence of measurement errors is a ubiquitously faced problem and plenty of work has been done to overcome this when a single covariate is mismeasured under a variety of conditions. However, in practice, it is possible that more than one covariate is measured with error. When measurements are taken by the same device, the errors of these measurements are likely correlated. In this paper, we present a novel approach to estimate the covariance matrix of classical additive errors in the absence of validation data or auxiliary variables when two covariates are subject to measurement error. Our method assumes these errors to be following a bivariate normal distribution. We show that the variance matrix is identiﬁable under certain conditions on the support of the error-free variables and propose an estimation method based on an expansion of Bernstein polynomials. To investigate the per- formance of the proposed estimation method, the asymptotic properties of the estimator are examined and a diverse set of simulation studies is con- ducted. The estimated matrix is then used by the simulation-extrapolation (SIMEX) algorithm to reduce the bias caused by measurement error in lo- gistic regression models. Finally, the method is demonstrated using data from the Framingham Heart Study.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47033673","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