Novel Methods for Estimation and Inference in Varying Coefficient Models

Abstract

Function type parameters relax many model assumptions because of the flexibility and the size of the parameter space. However, the curse of dimensionality has been the biggest challenge in the nonparametric regression area. An advantageous approach to dimension reduction is using basis expansion to approximate infinite parameter space. An even more challenging problem is estimating functions with unique structures, such as functions with zero-effect regions. The main part of this dissertation is working on varying coefficients with zero-effect regions. We propose a novel model that can detect zero-effect regions and estimate the non-zero effects simultaneously. We provide theoretical support for the inference of our proposed estimators. Simulation studies and real data analyses demonstrate the advantage of our models. This dissertation also introduces a new model that considers the additive effects from a novel aspect: estimating the dynamic effect changes. Simulations and real data applications provide comparisons between our model and the existing model.