Abstract
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.
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The authors are most grateful to the Editor and anonymous referees for carefully reading the manuscript and valuable suggestions which helped in improving an earlier version of this paper.
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Supported by the National Social Science Foundation of China (Grant No. 22BTJ059)
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Yao, Y.B., Lü, Y.T., Lu, C. et al. The Consistency of LSE Estimators in Partial Linear Regression Models under Mixing Random Errors. Acta. Math. Sin.-English Ser. (2023). https://doi.org/10.1007/s10114-023-1003-7
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DOI: https://doi.org/10.1007/s10114-023-1003-7