Semiparametric estimation for partially linear models with ψψ-weak dependent errors

Semiparametric estimators are developed for a partially linear regression model with ψψ-weakly dependent errors. The ψψ-weak dependence condition, introduced by Doukhan and Louhich [Doukhan, P., and Louhich, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications, 84, 313–342], unifies weak dependence conditions such as mixing, association, Gaussian sequences and Bernoulli shifts. The class of ψψ-weak dependent processes includes many important nonlinear processes such as stationary threshold autoregressive processes and bilinear processes as well as stationary ARMA processes. Asymptotic normalities are established for semiparametric generalized least squares estimators of the parametric component and for estimators of the nonparametric function. Expansions are obtained for the biases and variances of the estimators. Real data set and simulated data set analyses are provided for a model with a threshold autoregressive error process.