Let H+n(R) be the cone of all positive semidefinite n x real matrices. Two best known partial orders that were mostly studied on subsets square complex matrices are L?wner and minus orders. Motivated by applications in statistics we study these H+ (R). We describe form surjective maps (R), > 1, preserve order both directions. present an equivalent definition (R) also characterize surjective,...

Title of Dissertation: Nonparametric Quasi-likelihood in Longitudinal Data Analysis Xiaoping Jiang, Doctor of Philosophy, 2004 Dissertation directed by: Professor Paul J. Smith Statistics Program Department of Mathematics This dissertation proposes a nonparametric quasi-likelihood approach to estimate regression coefficients in the class of generalized linear regression models for longitudinal ...

Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our ap...

We discuss a new class of models for random covariance structures defined by probability distributions over sparse eigenmatrices. The decomposition of orthogonal square matrices in terms of Givens rotations defines a natural, interpretable framework for defining prior distributions over the sparsity structure of random eigenmatrices. We explore some theoretical aspects and implications for cond...

There is recent evidence from laboratory experiments and analysis of livestock populations that not only the phenotype itself, but also its environmental variance, is under genetic control. Little is known about the relationships between the environmental variance of one trait and mean levels of other traits, however. A genetic covariance between these is expected to lead to nonlinearity betwee...

Driven by a wide range of contemporary applications, statistical inference for covariance structures has been an active area of current research in high-dimensional statistics. This paper provides a selective survey of some recent developments in hypothesis testing for high-dimensional covariance structures, including global testing for the overall pattern of the covariance structures and simul...

This paper concerns matrix computations within algorithms for variance and covariance component estimation. Hemmerle and Hartley [Technometrics, 15 (1973), pp. 819-831 showed how to compute the objective function and its derivatives for maximum likelihood estimation of variance components using matrices with dimensions of the order of the number of coefficients rather than that of the number of...