Jackknife for nonlinear estimating equations

Abstract

In mixture with varying concentrations model (MVC) one deals with a nonhomogeneous sample which consists of subjects belonging to a fixed number of different populations (mixture components). The population which a subject belongs to is unknown, but the probabilities to belong to a given component are known and vary from observation to observation. The distribution of subjects’ observed features depends on the component which it belongs to. Generalized estimating equations (GEE) for Euclidean parameters in MVC models are considered. Under suitable assumptions the obtained estimators are asymptotically normal. A jackknife (JK) technique for the estimation of their asymptotic covariance matrices is described. Consistency of JK-estimators is demonstrated. An application to a model of mixture of nonlinear regressions and a real life example are presented.