In the paper three permutation tests of significance of variance components in the linear mixed model are presented. Two of them are permutation versions of classic tests. The third one is based on log-likelihood. In the Monte Carlo simulation studies properties of the permutation tests are compared with properties of the classic likelihood ratio test and Wald test.
The paper discusses studentized sample mean distribution. The sample is from exponential distribution. On the basis of independent replications of the samples empirical distributions studentized mean was calculated. The distance between the empirical distributions and the standard normal distribution was measured by means well known as statistics of Kolmogorov. Under the appropriate sample sizes the degree of the difference between the empirical and theoretical distributions was evaluated. Moreover, the hypothesis on normality of the empirical distributions was tested by means of the Kolmogorov test.
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