Consistency properties for the estimators of partially linear regression model under dependent errors

摘要

In this paper, we study the consistency properties for the partially linear regression model: where , and are known to be non-random, is an unknown continuous function on a compact set A in , are -mixing random errors with mean zero, are random variables which are observable at points and . By using the probability inequalities and moment inequalities, we obtain the strong consistency, complete consistency and mean consistency for the estimators and of beta and g, respectively. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.