廣義多參數概似模型之估計

Abstract

Multiparameter likelihood models (MLMs) with multiple covariates have a wide range of applications; however, they encounter the “curse of dimension- ality” problem when the dimension of the covariates is large. We develop a generalized multiparameter likelihood model that copes with multiple covari- ates and adapts to dynamic structural changes well. It includes some popular models, such as the partially linear and varying-coefficients models, as special cases. We discuss the backfitting and profile likelihood procedures and present a simple, effective two-step method to estimate both the parametric and the nonparametric components when the model is fixed. All these estimators of the parametric component has the n−1/2 convergence rate, and the estimator of the nonparametric component enjoys an adaptivity property. We suggest a data-driven procedure for selecting the bandwidths, and propose an initial estimator in backfitting and profile likelihood estimation of the parametric part to ensure stability of the approach in general settings. We further develop an automatic procedure to identify constant parameters in the underlying model. We provide several simulation studies and an application to infant mortality data of China to demonstrate the performance of our proposed method.