Estimation and testing for panel data partially linear single-index models with errors correlated in space and time

Abstract

We consider a panel data partially linear single-index models (PDPLSIM) with errors correlated in space and time. A serially correlated error structure is adopted for the correlation in time. We propose using a semiparametric minimum average variance estimation (SMAVE) to obtain estimators for both the parameters and unknown link function. We not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. Then, a fitting of spatial and time-wise correlation structures is investigated. Based on the estimators, we propose a generalized F-type test method to deal with testing problems of index parameters of PDPLSIM with errors correlated in space and time. It is shown that under the null hypothesis, the proposed test statistic follows asymptotically a [Formula: see text]-distribution with the scale constant and degrees of freedom being independent of nuisance parameters or functions. Simulated studies and real data examples have been used to illustrate our proposed methodology.

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

“…Moreover, the form of parametric regression models may be misspecified, and estimators based on misspecified models are able to cause inconsistency and even erroneous conclusions. Driven by these reasons, Zhao et al [18] constructed semiparametric minimum average variance estimation method, and proposed a F-test statistic of partially linear single-index panel regression model with separable space-time filters, then proved the asymptotic properties of estimators and test statistic. Bai, Hu, and You [19] established weighted semiparametric least squares and weighted polynomial spline series estimation method for parametric and nonparametric component, respectively, of panel data partially linear varying-coefficient regression model with separable space-time filters, and then proved their asymptotic normalities.…”