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Variable bandwidth kernel regression estimation. (English) Zbl 1466.62286

Summary: In this paper we propose a variable bandwidth kernel regression estimator for i.i.d. observations in \(\mathbb{R}^2\) to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of \(O(h_n^4)\) 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.

MSC:

62G07 Density estimation
62E20 Asymptotic distribution theory in statistics
62H12 Estimation in multivariate analysis
60F05 Central limit and other weak theorems

Software:

np
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References:

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