Bootstrap of a Semiparametric Partially Linear Model with Autoregressive Errors

This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable serially correlated random errors. The random errors are modeled by an autoregressive time series. We show that the distributions of the feasible semiparametric generalized least squares estimator of the parametric component, and the estimator of the autoregressive coefficients of the error process, admit bootstrap approximation. Simulation results show that the bootstrap substantially outperforms the normal approximation not only for small to medium sample sizes, but also for highly correlated random errors. A data example is provided to illustrate the method.