Impossibility of weak convergence of kernel density estimators to a non-degenerate law in L2(ℝd)

研究成果: Article査読

3 被引用数 (Scopus)

抄録

It is well known that the kernel estimator, for the probability density f on ℝd has pointwise asymptotic normality and that its weak convergence in a function space, especially with the uniform topology, is a difficult problem. One may conjecture that the weak convergence in L2(ℝd) could be possible. In this paper, we deny this conjecture. That is, letting, we prove that for any sequence {rn} of positive constants such that rn = o(√n), if the rescaled residual, converges weakly to a Borel limit in L2(ℝd), then the limit is necessarily degenerate.

本文言語English
ページ(範囲)129-135
ページ数7
ジャーナルJournal of Nonparametric Statistics
23
1
DOI
出版ステータスPublished - 2011 3 1
外部発表はい

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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