Flexible generalized varying coefficient regression models

TL;DR

This paper introduces a highly flexible nonparametric regression model that unifies various existing models, providing interpretable effects of covariates and applicable to diverse data types, supported by theoretical analysis and simulations.

Contribution

It develops a general framework for flexible multivariate regression, establishes estimation equivalence, and proposes a kernel-based estimator with an iterative solution and theoretical guarantees.

Findings

Kernel estimator solves nonlinear integral equations

Iterative algorithm converges with theoretical properties

Simulation results demonstrate model effectiveness

Abstract

This paper studies a very flexible model that can be used widely to analyze the relation between a response and multiple covariates. The model is nonparametric, yet renders easy interpretation for the effects of the covariates. The model accommodates both continuous and discrete random variables for the response and covariates. It is quite flexible to cover the generalized varying coefficient models and the generalized additive models as special cases. Under a weak condition we give a general theorem that the problem of estimating the multivariate mean function is equivalent to that of estimating its univariate component functions. We discuss implications of the theorem for sieve and penalized least squares estimators, and then investigate the outcomes in full details for a kernel-type estimator. The kernel estimator is given as a solution of a system of nonlinear integral equations. We provide an iterative algorithm to solve the system of equations and discuss the theoretical properties of the estimator and the algorithm. Finally, we give simulation results.