A test for abrupt change in hazard regression models with Weibull baselines

We develop a likelihood ratio test for an abrupt change point in Weibull hazard functions with covariates, including the two-piece constant hazard as a special case. We first define the log-likelihood ratio test statistic as the supremum of the profile log-likelihood ratio process over the interval which may contain an unknown change point. Using local asymptotic normality (LAN) and empirical measure, we show that the profile log-likelihood ratio process converges weakly to a quadratic form of Gaussian processes. We determine the critical values of the test and discuss how the test can be used for model selection. We also illustrate the method using the Chronic Granulomatous Disease (CGD) data.     

A likelihood ratio test for bimodality in two-component mixtures with application to regional income distribution in the EU

We propose a parametric test for bimodality based on the likelihood principle by using two-component mixtures. The test uses explicit characterizations of the modal structure of such mixtures in terms of their parameters. Examples include the univariate and multivariate normal distributions and the von Mises distribution. We present the asymptotic distribution of the proposed test and analyze its finite sample performance in a simulation study. To illustrate our method, we use mixtures to investigate the modal structure of the cross-sectional distribution of per capita log GDP across EU regions from 1977 to 1993. Although these mixtures clearly have two components over the whole time period, the resulting distributions evolve from bimodality toward unimodality at the end of the 1970s.