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Journal of Multivariate Analysis

Mengyan Li, Yanyuan Ma, Runze Li
Covariate measurement error is a common problem. Improper treatment of measurement errors may affect the quality of estimation and the accuracy of inference. Extensive literature exists on homoscedastic measurement error models, but little research exists on heteroscedastic measurement. In this paper, we consider a general parametric regression model allowing for a covariate measured with heteroscedastic error. We allow both the variance function of the measurement errors and the conditional density function of the error-prone covariate given the error-free covariates to be completely unspecified...
May 2019: Journal of Multivariate Analysis
Cen Wu, Qingzhao Zhang, Yu Jiang, Shuangge Ma
With its important biological implications, modeling the associations of gene expression (GE) and copy number variation (CNV) has been extensively conducted. Such analysis is challenging because of the high data dimensionality, lack of knowledge regulating CNVs for a specific GE, different behaviors of the cis -acting and trans -acting CNVs, possible long-tailed distributions and contamination of GE measurements, and correlations between CNVs. The existing methods fail to address one or more of these challenges...
November 2018: Journal of Multivariate Analysis
Linlin Dai, Kani Chen, Zhihua Sun, Zhenqiu Liu, Gang Li
This paper studies the asymptotic properties of a sparse linear regression estimator, referred to as broken adaptive ridge (BAR) estimator, resulting from an L 0 -based iteratively reweighted L 2 penalization algorithm using the ridge estimator as its initial value. We show that the BAR estimator is consistent for variable selection and has an oracle property for parameter estimation. Moreover, we show that the BAR estimator possesses a grouping effect: highly correlated covariates are naturally grouped together, which is a desirable property not known for other oracle variable selection methods...
November 2018: Journal of Multivariate Analysis
Ming-Yueh Huang, Kwun Chuen Gary Chan
The estimation of continuous treatment effect functions using observational data often requires parametric specification of the effect curves, the conditional distributions of outcomes and treatment assignments given multi-dimensional covariates. While nonparametric extensions are possible, they typically suffer from the curse of dimensionality. Dimension reduction is often inevitable and we propose a sufficient dimension reduction framework to balance parsimony and flexibility. The joint central subspace can be estimated at a n 1/2 -rate without fixing its dimension in advance, and the treatment effect function is estimated by averaging local estimates of a reduced dimension...
November 2018: Journal of Multivariate Analysis
David Hong, Laura Balzano, Jeffrey A Fessler
Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding its performance for data that are both high-dimensional and heteroscedastic. This paper analyzes the statistical performance of PCA in this setting, i.e., for high-dimensional data drawn from a low-dimensional subspace and degraded by heteroscedastic noise. We provide simplified expressions for the asymptotic PCA recovery of the underlying subspace, subspace amplitudes and subspace coefficients; the expressions enable both easy and efficient calculation and reasoning about the performance of PCA...
September 2018: Journal of Multivariate Analysis
Siliang Gong, Kai Zhang, Yufeng Liu
Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression (LARS), among others. These methods typically add variables into the model one by one. For such selection procedures, it is crucial to find a stopping criterion that controls model complexity. One of the most commonly used techniques to this end is cross-validation (CV) which, in spite of its popularity, has two major drawbacks: expensive computational cost and lack of statistical interpretation...
July 2018: Journal of Multivariate Analysis
Sheng Fu, Sanguo Zhang, Yufeng Liu
Large-margin classifiers are powerful techniques for classification problems. Although binary large-margin classifiers are heavily studied, multicategory problems are more complicated and challenging. A common approach is to construct k different decision functions for a k -class problem with a sum-to-zero constraint. However, such a constraint can be inefficient. Moreover, many large-margin classifiers can be sensitive to outliers in the training sample. In this article, we use the angle-based classification framework to avoid the explicit sum-to-zero constraint, and we propose two adaptively weighted large-margin classification techniques...
July 2018: Journal of Multivariate Analysis
Sihai Dave Zhao, T Tony Cai, Hongzhe Li
It is frequently of interest to jointly analyze two paired sequences of multiple tests. This paper studies the problem of detecting whether there are more pairs of tests that are significant in both sequences than would be expected by chance. The asymptotic detection boundary is derived in terms of parameters such as the sparsity of non-null cases in each sequence, the effect sizes of the signals, and the magnitude of the dependence between the two sequences. A new test for detecting weak dependence is also proposed, shown to be asymptotically adaptively optimal, studied in simulations, and applied to study genetic pleiotropy in 10 pediatric autoimmune diseases...
August 2017: Journal of Multivariate Analysis
Gyuhyeong Goh, Dipak K Dey, Kun Chen
Many modern statistical problems can be cast in the framework of multivariate regression, where the main task is to make statistical inference for a possibly sparse and low-rank coefficient matrix. The low-rank structure in the coefficient matrix is of intrinsic multivariate nature, which, when combined with sparsity, can further lift dimension reduction, conduct variable selection, and facilitate model interpretation. Using a Bayesian approach, we develop a unified sparse and low-rank multivariate regression method to both estimate the coefficient matrix and obtain its credible region for making inference...
May 2017: Journal of Multivariate Analysis
Quefeng Li, Menggang Yu, Sijian Wang
In the era of big data, integrative analyses that pool data from different sources are now extensively conducted in order to improve performance. Among many interesting applications, genomics research is an area where integrative methods become popular tools to identify prognostic biomarkers for various diseases. In this paper, we propose such a framework for pathway and gene identification. Our method employs a hierarchical decomposition on genes' effects followed by a proper regularization to identify important pathways and genes across multiple studies...
April 2017: Journal of Multivariate Analysis
Jichun Xie, Jian Kang
Exploring resting-state brain functional connectivity of autism spectrum disorders (ASD) using functional magnetic resonance imaging (fMRI) data has become a popular topic over the past few years. The data in a standard brain template consist of over 170,000 voxel specific points in time for each human subject. Such an ultra-high dimensionality makes the voxel-level functional connectivity analysis (involving four billion voxel pairs) both statistically and computationally inefficient. In this work, we introduce a new framework to identify the functional brain network at the anatomical region level for each individual...
April 2017: Journal of Multivariate Analysis
T Tony Cai, Anru Zhang
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions...
September 2016: Journal of Multivariate Analysis
Rolando De la Cruz, Cristian Meza, Ana Arribas-Gil, Raymond J Carroll
Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary response. They provide a useful way to assess association between these two kinds of data, which in clinical studies are often collected jointly on a series of individuals and may help understanding, for instance, the mechanisms of recovery of a certain disease or the efficacy of a given therapy...
January 2016: Journal of Multivariate Analysis
Chenxi Li
We consider semiparametric analysis of competing risks data subject to mixed case interval censoring. The Fine-Gray model (Fine & Gray, 1999) is used to model the cumulative incidence function and is coupled with sieve semiparametric maximum likelihood estimation based on univariate or multivariate likelihood. The univariate likelihood of cause-specific data enables separate estimation of cumulative incidence function for each competing risk, in contrast with the multivariate likelihood of full data which estimates cumulative incidence functions for multiple competing risks jointly...
January 1, 2016: Journal of Multivariate Analysis
T Tony Cai, Anru Zhang
Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices...
January 1, 2016: Journal of Multivariate Analysis
Larissa A Matos, Dipankar Bandyopadhyay, Luis M Castro, Victor H Lachos
In biomedical studies on HIV RNA dynamics, viral loads generate repeated measures that are often subjected to upper and lower detection limits, and hence these responses are either left- or right-censored. Linear and non-linear mixed-effects censored (LMEC/NLMEC) models are routinely used to analyse these longitudinal data, with normality assumptions for the random effects and residual errors. However, the derived inference may not be robust when these underlying normality assumptions are questionable, especially the presence of outliers and thick-tails...
October 1, 2015: Journal of Multivariate Analysis
David Gerard, Peter Hoff
Inference about dependencies in a multiway data array can be made using the array normal model, which corresponds to the class of multivariate normal distributions with separable covariance matrices. Maximum likelihood and Bayesian methods for inference in the array normal model have appeared in the literature, but there have not been any results concerning the optimality properties of such estimators. In this article, we obtain results for the array normal model that are analogous to some classical results concerning covariance estimation for the multivariate normal model...
May 1, 2015: Journal of Multivariate Analysis
Belmiro P M Duarte, Weng Kee Wong, Anthony C Atkinson
T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach...
March 2015: Journal of Multivariate Analysis
Solomon W Harrar, Xiaoli Kong
In this paper, test statistics for repeated measures design are introduced when the dimension is large. By large dimension is meant the number of repeated measures and the total sample size grow together but either one could be larger than the other. Asymptotic distribution of the statistics are derived for the equal as well as unequal covariance cases in the balanced as well as unbalanced cases. The asymptotic framework considered requires proportional growth of the sample sizes and the dimension of the repeated measures in the unequal covariance case...
March 2015: Journal of Multivariate Analysis
Weidong Liu, Xi Luo
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm...
March 1, 2015: Journal of Multivariate Analysis
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