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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
Seonjin Kim, Zhibiao Zhao, Xiaofeng Shao
This paper is concerned with the inference of nonparametric mean function in a time series context. The commonly used kernel smoothing estimate is asymptotically normal and the traditional inference procedure then consistently estimates the asymptotic variance function and relies upon normal approximation. Consistent estimation of the asymptotic variance function involves another level of nonparametric smoothing. In practice, the choice of the extra bandwidth parameter can be difficult, the inference results can be sensitive to bandwidth selection and the normal approximation can be quite unsatisfactory in small samples leading to poor coverage...
January 1, 2015: Journal of Multivariate Analysis
Xiao-Feng Wang, Deping Ye
This paper is motivated by a wide range of background correction problems in gene array data analysis, where the raw gene expression intensities are measured with error. Estimating a conditional density function from the contaminated expression data is a key aspect of statistical inference and visualization in these studies. We propose re-weighted deconvolution kernel methods to estimate the conditional density function in an additive error model, when the error distribution is known as well as when it is unknown...
January 1, 2015: Journal of Multivariate Analysis
Rosanna Overholser, Ronghui Xu
The effective degrees of freedom is a useful concept for describing model complexity. Recently the number of effective degrees of freedom has been shown to relate to the concept of conditional Akaike information (cAI) in the mixed effects models. This relationship was made explicit under linear mixed-effects models with i.i.d. errors, and later also extended to the generalized linear and the proportional hazards mixed models. We show that under linear mixed-effects models with correlated errors, the number of effective degrees of freedom is asymptotically equal to the trace of the usual `hat' matrix plus the number of parameters in the error covariance matrix...
November 1, 2014: Journal of Multivariate Analysis
Ruosha Li, Limin Peng
Semi-competing risks data frequently arise in biomedical studies when time to a disease landmark event is subject to dependent censoring by death, the observation of which however is not precluded by the occurrence of the landmark event. In observational studies, the analysis of such data can be further complicated by left truncation. In this work, we study a varying co-efficient subdistribution regression model for left-truncated semi-competing risks data. Our method appropriately accounts for the specifical truncation and censoring features of the data, and moreover has the flexibility to accommodate potentially varying covariate effects...
October 1, 2014: Journal of Multivariate Analysis
Seonjin Kim, Zhibiao Zhao
Most existing works on specification testing assume that we have direct observations from the model of interest. We study specification testing for Markov models based on contaminated observations. The evolving model dynamics of the unobservable Markov chain is implicitly coded into the conditional distribution of the observed process. To test whether the underlying Markov chain follows a parametric model, we propose measuring the deviation between nonparametric and parametric estimates of conditional regression functions of the observed process...
September 2014: Journal of Multivariate Analysis
Y Wang, M J Daniels
In this article, we propose a computationally efficient approach to estimate (large) p-dimensional covariance matrices of ordered (or longitudinal) data based on an independent sample of size n. To do this, we construct the estimator based on a k-band partial autocorrelation matrix with the number of bands chosen using an exact multiple hypothesis testing procedure. This approach is considerably faster than many existing methods and only requires inversion of (k + 1)-dimensional covariance matrices. The resulting estimator is positive definite as long as k < n (where p can be larger than n)...
September 1, 2014: Journal of Multivariate Analysis
Jian-Lun Xu
When an n × 1 random vector X = (X 1, …, Xn ) (T) has a sign-invariant distribution, Strait [J. Multivariate Anal. 4 (1974) 494-496] proved that the expectations of max(0, X 1, X 1 + X 2, …, X 1 + Xn ) and max(0, X 1, …, Xn ) are equal. In this note we assume a weaker condition that (X 1, X 2, …, Xn ) and (-X 1, X 2, …, Xn ) are equal in distribution and prove a more general result that the expectations of Lr (0, X 1, X 1 + X 2, …, X 1 + Xn ) and Lr (0, X 1, …, Xn ) are equal, where Lr (0, X 1, …, Xn ) is the rth order statistic of 0, X 1, …, Xn for r = 1, …, n + 1...
August 1, 2014: Journal of Multivariate Analysis
Joshua D Habiger, Edsel A Peña
Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently been shown that these types of multiple testing procedures are inefficient since such p-values do not depend upon all of the available data. This paper provides tools for constructing compound p-value statistics, which are those that depend upon all of the available data, but still satisfy the conditions of independence and uniformity under the null hypotheses...
April 1, 2014: Journal of Multivariate Analysis
Kurt Hornik, Bettina Grün
Diaconis and Ylvisaker (1979) give necessary conditions for conjugate priors for distributions from the natural exponential family to be proper as well as to have the property of linear posterior expectation of the mean parameter of the family. Their conditions for propriety and linear posterior expectation are also sufficient if the natural parameter space is equal to the set of all [Formula: see text]-dimensional real numbers. In this paper their results are extended to characterize when conjugate priors are proper if the natural parameter space is bounded...
April 2014: Journal of Multivariate Analysis
Subhash Aryal, Dulal K Bhaumik, Thomas Mathew, Robert D Gibbons
In this article we derive an optimal test for testing the significance of covariance matrices of random-effects of two multivariate mixed-effects linear models. We compute the power of this newly derived test via simulation for various alternative hypotheses in a bivariate set up for unbalanced designs and observe that power responds sharply when sample size and alternative hypotheses are changed. For some balanced designs we compare power of the optimal test to that of the likelihood ratio test via simulation, and find that the proposed test has greater power than the likelihood ratio test...
February 2014: Journal of Multivariate Analysis
Leslie Cope, Daniel Q Naiman, Giovanni Parmigiani
The integrative correlation coefficient was developed to facilitate the validation of expression microarray results in public datasets, by identifying genes that are reproducibly measured across studies and even across microarray platforms. In the current study, we develop a number of interesting and important mathematical and statistical properties of the integrative correlation coefficient, including a unique permutation-based null distribution with the unusual property that the variance does not shrink as the sample size increases, discussing how these findings impact its use and interpretation, and what they have to say about any method for identifying reproducible genes in a meta-analysis...
January 1, 2014: Journal of Multivariate Analysis
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