On kernel estimation of a multivariate distribution function

Zhezhen Jin and Yongzhao Shao

Statistics & Probability Letters, 1999, vol. 41, issue 2, 163-168

Abstract: The optimal bandwidth of the d-dimensional kernel estimator of a density is well known to have order n-1/(4+d. In this note, the multivariate distribution function F(x) is estimated by integrating a kernel estimator of its density. The asymptotic optimal bandwidth of the d-dimensional kernel distribution estimator of F(x) is shown to have order n-1/3, for all dimensions d and at all points x except those satisfying the Laplace equation [Delta]F(x) = 0.

Keywords: Kernel; estimator; Optimal; bandwidth; Mean; squared; error (search for similar items in EconPapers)
Date: 1999
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