Швидкi розрахунки оцiнок коварiацiйних матриць методом складаного ножа

Abstract

We consider data in which each observed subject belongs to one of different subpopulations (components). The true number of component which a subject belongs to is unknown, but the researcher knows the probabilities that a subject belongs to a given component (concentration of the component in the mixture). The concentrations are different for different observations. So the distribution of the observed data is a mixture of components’ distributions with varying concentrations. A set of variables is observed for each subject. Dependence between these variables is described by a nonlinear regression model. The coefficients of this model are different for different components. Normality of estimator for nonlinear regression parameters is demonstrated under general assumptions. A mixture of logistic regression models with continuous response is considered as an example. In the paper we construct confidence ellipsoids for the regression parameters based on the modified least squares estimators. The covariances of these estimators are estimated by the multiple modifications of jackknife technique. Performance of the obtained confidence ellipsoids is assessed by simulations.