The Consistency of LSE Estimators in Partial Linear Regression Models under Mixing Random Errors

In this paper, we consider the partial linear regression model y(i) = x(i)beta* + g(t(i)) + epsilon(i), i = 1, 2, ..., n, where (x(i), t(i)) are known fixed design points, g(center dot) is an unknown function, and beta* is an unknown parameter to be estimated, random errors epsilon(i) are (alpha, beta)-mixing random variables. The p-th (p > 1) mean consistency, strong consistency and complete consistency for least squares estimators of beta* and g(center dot) are investigated under some mild conditions. In addition, a numerical simulation is carried out to study the finite sample performance of the theoretical results. Finally, a real data analysis is provided to further verify the effect of the model.