Linear Covariance Structure Research Articles

HYPOTHESIS TESTING ON LINEAR STRUCTURES OF HIGH DIMENSIONAL COVARIANCE MATRIX.

This paper is concerned with test of significance on high dimensional covariance structures, and aims to develop a unified framework for testing commonly-used linear covariance structures. We first construct a consistent estimator for parameters involved in the linear covariance structure, and then develop two tests for the linear covariance structures based on entropy loss and quadratic loss used for covariance matrix estimation. To study the asymptotic properties of the proposed tests, we study related high dimensional random matrix theory, and establish several highly useful asymptotic results. With the aid of these asymptotic results, we derive the limiting distributions of these two tests under the null and alternative hypotheses. We further show that the quadratic loss based test is asymptotically unbiased. We conduct Monte Carlo simulation study to examine the finite sample performance of the two tests. Our simulation results show that the limiting null distributions approximate their null distributions quite well, and the corresponding asymptotic critical values keep Type I error rate very well. Our numerical comparison implies that the proposed tests outperform existing ones in terms of controlling Type I error rate and power. Our simulation indicates that the test based on quadratic loss seems to have better power than the test based on entropy loss.

Effective Sample Size for Line Transect Sampling Models with an Application to Marine Macroalgae

This paper provides a framework for estimating the effective sample size in a spatial regression model context when the data have been sampled using a line transect scheme and there is an evident serial correlation due to the chronological order in which the observations were collected. We propose a linear regression model with a partially linear covariance structure to address the computation of the effective sample size when spatial and serial correlations are present. A recursive algorithm is described to separately estimate the linear and nonlinear parameters involved in the covariance structure. The kriging equations are also presented to explore the kriging variance between our proposal and a typical spatial regression model. An application in the context of marine macroalgae, which motivated the present work, is also presented.

An improved approximation to the precision of fixed effects from restricted maximum likelihood

An approximate small sample variance estimator for fixed effects from the multivariate normal linear model, together with appropriate inference tools based on a scaled F pivot, is now well established in practice and there is a growing literature on its properties in a variety of settings. Although effective under linear covariance structures, there are examples of nonlinear structures for which it does not perform as well. The cause of this problem is shown to be a missing term in the underlying Taylor series expansion which accommodates the bias in the estimators of the parameters of the covariance structure. The form of this missing term is derived, and then used to adjust the small sample variance estimator. The behaviour of the resulting estimator is explored in terms of invariance under transformation of the covariance parameters and also using a simulation study. It is seen to perform successfully in the way predicted from its derivation.

Health, health care, and the environment. Econometric evidence from German micro data.

The paper develops and applies a Grossman-style health production model set up in discrete time to explain the impact of environmental pollution on the demand for both health and health care. In order to introduce the environment, our analysis takes changes in environmental conditions to influence the rate at which an individual's stock of health depreciates. While the theoretical part of our paper also contains a discussion of the full model, we restrict our empirical analysis to a submodel which is known as the pure investment model. This is because the other submodel, the pure consumption model, implies a rather implausible case of satiation with respect to the individual's preferences. Our empirical findings are based on data taken from the German Socio-economic Panel. The stock of health capital and environmental pollution are treated as latent variables and estimated using a Linear Covariance Structures model. The quality of the environment turns out to be an important determinant of health capital. From the point of view of health economics, improvements in environmental conditions can be interpreted as preventive measures. In terms of prevention, public policies designed to protect the environment also yield significant health effects. As regards health care demand the influence is not clearcut, i.e., one cannot necessarily expect a reduction in resource use.

A mixed linear model with linear covariance structure: a sensitivity analysis of maximum likelihood estimators

Incomplete and mistimed longitudinal data are common problems in longitudinal studies of free living populations. One possible approach to the analysis of longitudinal data with randomly missing or mistimed data uses a mixed effects model. While the theory underlying this approach is not new (Harville, 1977), very little has been published about its actual application. The objective of this paper is to examine the behavior of the maximum likelihood estimates of mixed effects model parameters when the distribution of the parameters underlying the data is known. Specifically, the effects of different values of the error covariance parameters and missing and mistimed data are considered. Two iterative methods, the Method of Scoring and the EM algorithm, were utilized to solve the maximum likelihood equations. In the setting considered here, the Method of Scoring and the EM algorithm worked well for the analysis of longitudinal data with missing and/or mistimed data. The variance of the parameter estimates in...

Contributions to-asymptotic theory in regression models with linear covariance structure1

Asymptotic results are .presented- for estimating the parameters in variance-components models both with linear and with nonlinear regression functions.