A Likelihood Ratio Test for Separability of Covariances

• Activity Number: 168
• Type: Contributed
• Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics & the Environment
• Author(s): Matthew Mitchell*+ and Marc G. Genton and Marcia L. Gumpertz
• Companies: Becton, Dickinson and Company and North Carolina State University and North Carolina State University
• Keywords: FACE experiments ; Kronecker product ; multivariate repeated measures ; separable covariance ; spatio-temporal process

Abstract

A common way to model spatio-temporal covariances is with separable models, where the joint space-time covariance factors into the product of a covariance function that depends only on space and a covariance function that depends only on time. This greatly reduces the number of parameters, and thus makes estimation computationally much easier. We propose a formal test of separability based on a likelihood ratio statistic. The test is developed in the context of a replicated spatio-temporal process or more generally in the context of multivariate repeated measures (for example, several variables measured at multiple times on many subjects). When the null hypothesis of separability holds, the value of the test statistic does not depend on the type of separable model. Thus, it is possible to develop reference distributions of the test statistic under the null hypothesis. The test does not require second-order stationarity, isotropy, or specification of a covariance model. This test can be adapted to the case when there is one replicate by creating pseudo-replicates. The test is applied to an environmental monitoring data set.