Estimation and Testing of Random Effects Semiparametric Regression Model with Separable Space-Time Filters

This paper focuses on studying a random effects semiparametric regression model (RESPRM) with separable space-time filters. The model cannot only capture the linearity and nonlinearity existing in a space-time dataset, but also avoid the inefficient estimators caused by ignoring spatial correlation and serial correlation in the error term of a space-time data regression model. Its profile quasi-maximum likelihood estimators (PQMLE) for parameters and nonparametric functions, and a generalized F-test statistic for checking the existence of nonlinear relationships are constructed. The asymptotic properties of estimators and asymptotic distribution of test statistic are derived. Monte Carlo simulations imply that our estimators and test statistic have good finite sample performance. The Indonesian rice farming data are used to illustrate our methods.