Semiparametric mixture of binomial regression with a degenerate component

Abstract

Many historical datasets contain a large number of zeros, and cannot be modeled directly using a single distribution. Motivated by rain data from a global climate model, we study a semiparametric mixture of binomial regression, in which both the component proportions and the success probabilities depend on the predictors nonparametrically. An EM algorithm is proposed to estimate this semiparametric mixture model by maximizing the local likelihood function. We also consider a special case in which the component proportions are constant while the component success probabilities still depend on the predictors nonparametrically. This model is estimated by a one-step backfitting procedure, and the estimates are shown to achieve the optimal convergence rates. The asymptotic properties of the estimates for both models are established. The proposed procedures are demonstrated by modelling rain data from a global climate model and historical rain data from Edmonton, Canada. Simulation studies show that satisfactory estimates are obtained for the proposed models for finite samples.