On Estimation Methods in Generalized Multiparameter Likelihood Model
Date Issued
2010
Date
2010
Author(s)
Chen, Lu-Hung
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.
Subjects
Bandwidth selection
Model selection
Multiple covariate
Partially linear model
Backfitting
Pro?le likelihood
Varying-coef?cient model
Semiparametric models
SDGs
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