Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1146662 | Journal of Multivariate Analysis | 2011 | 14 Pages |
Abstract
Multivariate tree-indexed Markov processes are discussed with applications. A Galton–Watson super-critical branching process is used to model the random tree-indexed process. Martingale estimating functions are used as a basic framework to discuss asymptotic properties and optimality of estimators and tests. The limit distributions of the estimators turn out to be mixtures of normals rather than normal. Also, the non-null limit distributions of standard test statistics such as Wald, Rao’s score, and likelihood ratio statistics are shown to have mixtures of non-central chi-square distributions. The models discussed in this paper belong to the local asymptotic mixed normal family. Consequently, non-standard limit results are obtained.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Numerical Analysis
Authors
S.Y. Hwang, I.V. Basawa,