On some aspects of the optimal statistical inference on variance components in mixed linear models

Rok, strany: 2003, 133 - 153

In the paper the problem of hypotheses testing and interval estimation for variance components in mixed linear models is considered. Mostly, the optimal statistical inference is determined by giving the uniformly most powerful (invariant or unbiased or invariant unbiased) tests (UMPIT, UMPUT or UMPIUT, respectively) or by appropriate construction of the uniformly most accurate confidence intervals (UMACI). When the UMPIT does not exist a construction of the locally best invariant unbiased test (LBIUT) for a single variance component (or for a ratio of variance components) as a basis of the optimal statistical inference is given. The major objective of this article is, on the one hand, to present strict relationships between statistical tests and confidence intervals for select functions of variance components and, on the other hand, to answer the question: whether the confidence intervals or hypotheses tests are more informative for making decisions based on parametric values? Moreover, some aspects connected with the layouts with minimal number observations that assure existence of the uniformly best unbiased estimators (UBUE) and the UMPIT for variance components are considered. The designs with different degree of data imbalance for which the optimal statistical inference based on UMPIT or UMPIUT becomes impossible, are also presented. Theoretical considerations by a simulations study for some experimental layouts are illustrated, too.

ISO 690:

Michalski, A. 2003. On some aspects of the optimal statistical inference on variance components in mixed linear models. In Tatra Mountains Mathematical Publications, vol. 26, no.1, pp. 133-153. 1210-3195.

APA:

Michalski, A. (2003). On some aspects of the optimal statistical inference on variance components in mixed linear models. Tatra Mountains Mathematical Publications, 26(1), 133-153. 1210-3195.