SUMMARY. Likelihood ratio tests are used to test ordered hypotheses involving the parameters of k independent samples from an exponential family. For the test of constancy of the parameters versus an ordered alternative, the likelihood ratio test statistic is asymptotically distributed as a mixture of k chi-squared distributions under the null hypothesis. This paper derives an asymptotic expans...

This paper investigates the asymptotic properties of the likelihood ratio statistic for testing homogeneity in normal mixture models in the presence of a structural parameter. The asymptotic null distributions of the ordinary likelihood ratio statistic and the modified likelihood ratio statistic are the same, having the probability density function(pdf) (1/2)g1(x)+(1/2)g2(x) where g1(x) and g2(...

Wepropose a new and simple estimating equation for the parameters inmedian regression modelswith designed censoring variables, and then apply the empirical log likelihood ratio statistic to construct confidence region for the parameters. The empirical log likelihood ratio statistic is shown to have a standard chi-square distribution, which makes this method easy to implement. At the same time, ...