Multiparameter likelihood models (MLMs) with multiple covariates have a wide range of applications: however. they encounter the "curse of dimensionality" problem when the dimension of the covariates is large. We develop a generalized multiparameter likelihood model that copes with multiple covariates and adapts to dynamic structural changes well. It includes some popular models, such as the partially linear and varying-coefficient models, as special cases. We present a simple, effective two-step method to estimate both the parametric and the nonparametric components when the model is fixed. The proposed estimator 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 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 a simulation study and an application to infant mortality data of China to demonstrate the performance of our proposed method.
Cheng, M. Y., Zhang, W. Y., & Chen, L. H. (2009). Statistical estimation in generalized multiparameter likelihood models. Journal of the American Statistical Association, 104(487), 1179-1191. https://doi.org/10.1198/jasa.2009.tm08430