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

In this paper, we consider the partial linear regression model yi = xiβ* + g(ti) + εi, i = 1, 2, …, n, where (xi, ti) are known fixed design points, g(·) is an unknown function, and β* is an unknown parameter to be estimated, random errors εi are (α, β)-mixing random variables. The p-th (p > 1) mean consistency, strong consistency and complete consistency for least squares estimators of β* and g(·) 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.