Tests of hypotheses on quantiles of distributions of components in a mixture
Rostyslav Maiboroda, Olena Sugakova · Theory of Probability and Mathematical Statistics · 2021
The problem of testing statistical hypotheses concerning quantiles of different distributions of components in a mixture with varying concentrations is considered. Homogeneity of medians or that of interquartile ranges in different components are two possible examples of such kind of hypotheses. Estimators for quantiles in a model of mixtures with varying concentrations are presented. Sufficient conditions for the asymptotic normality of these estimators are obtained. Asymptotic confidence ellipsoids and tests for linear hypotheses based on these estimators are constructed. The quality of procedures proposed in this paper is checked for samples of finite sizes with the help of simulation results.