Hypothesis testing in unbalanced two-fold nested random models

Marcin Przystalski¹

¹ The Research Centre for Cultivar Testing 63-022 Słupia Wielka, Poland

Applicationes Mathematicae, Tome 43 (2016) no. 1, pp. 57-78

Résumé

In many applications of linear random models to multilevel data, it is of interest to test whether the random effects variance components are zero. In this paper we propose approximate tests for testing significance of variance components in the unbalanced two-fold nested random model in the presence of non-normality. In the derivations of the asymptotic distributions of the test statistics, as an intermediate result, the explicit form of the asymptotic covariance matrix of the vector of mean squares in this model is obtained. We also study the influence of some special type of designs on the asymptotic covariance matrix and on the distribution of the proposed test statistics.

Détail

DOI : 10.4064/am2274-1-2016

Keywords: many applications linear random models multilevel interest test whether random effects variance components zero paper propose approximate tests testing significance variance components unbalanced two fold nested random model presence non normality derivations asymptotic distributions test statistics intermediate result explicit form asymptotic covariance matrix vector mean squares model obtained study influence special type designs asymptotic covariance matrix distribution proposed test statistics