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On kernel estimation of a multivariate distribution function

✍ Scribed by Zhezhen Jin; Yongzhao Shao

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
229 KB
Volume
41
Category
Article
ISSN
0167-7152

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✦ Synopsis

The optimal bandwidth of the d-dimensional kernel estimator of a density is well known to have order n l.,(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 AF(x)= 0.

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