Quantile estimators for regression errors in mixture models with varying concentrations
Rostyslav Maiboroda, Vitaliy Miroshnychenko, Olena Sugakova · Bulletin of Taras Shevchenko National University of Kyiv Series Physics and Mathematics · 2024
In this paper we consider data obtained from a mixture of M different sub-populations (mixture components). Dependencies between the observed variables are described by nonlinear regression models with unknown regression parameters and error terms distributions different for different components. The mixing probabilities (concentrations of the components in the mixture) vary from observation to observation. Estimators for quantiles of error terms distributions are considered based on weighted empirical distribution functions of the regression models residuals. Consistency of these estimators is demonstrated. The results can be applied to the construction of quantile vs. quantile plots for visual comparison and analysis of error terms distributions.