Volume 25, 2021
|Page(s)||55 - 86|
|Published online||04 March 2021|
Variable bandwidth kernel regression estimation
Department of Mathematics, University of Central Arkansas,
AR 72035, USA.
2 Department of Mathematics, The University of Mississippi, University, MS 38677, USA.
3 Division of Arts and Sciences, Mississippi State University at Meridian, Meridian, MS 39307, USA.
* Corresponding author: email@example.com
Accepted: 12 January 2021
In this paper we propose a variable bandwidth kernel regression estimator for i.i.d. observations in ℝ2 to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of O(hn4) under the condition that the fifth order derivative of the density function and the sixth order derivative of the regression function are bounded and continuous. We also establish the central limit theorems for the proposed ideal and true variable kernel regression estimators. The simulation study confirms our results and demonstrates the advantage of the variable bandwidth kernel method over the classical kernel method.
Mathematics Subject Classification: 62G07 / 62E20 / 62H12
Key words: Kernel regression estimation / variable bandwidth / bias reduction / central limit theorem
© EDP Sciences, SMAI 2021
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