Estimation and testing for fixed effects partially linear nonparametric panel regression model with separable spatially and serially correlated error structure

Abstract

Panel data collected from “locations” may exhibit spatial and serial correlations. In order to study such spatial and serial correlations, and possible existing nonlinear relationships, a fixed effects partially linear nonparametric panel regression model with separable spatially and serially correlated error structure is introduced. We obtain profile quasi-maximum likelihood estimators (PQMLEs) of the unknowns. Furthermore, a generalized F-test called $F_{NT}$ is designed for assessing the reasonability of nonparametric component setting. Asymptotic properties of PQMLEs and $F_{NT}$ are provided under several conditions. Monte Carlo trials imply our estimators and test statistic exhibit good performance in finite samples and model misspecification may lead to substantial influence on the estimates of unknown parameters. The analysis of provincial housing price in China reveals the presence of nonlinear, spatial and serial correlation relationships.