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  • 标题:A note on the asymptotic law of the histogram without continuity assumptions
  • 本地全文:下载
  • 作者:Thomas Laloë ; Rémi Servien
  • 期刊名称:Brazilian Journal of Probability and Statistics
  • 印刷版ISSN:0103-0752
  • 出版年度:2016
  • 卷号:30
  • 期号:4
  • 页码:562-569
  • DOI:10.1214/15-BJPS294
  • 语种:English
  • 出版社:Brazilian Statistical Association
  • 摘要:Asymptotic normality of density estimates often requires the continuity of the underlying density and assumptions on its derivatives. Recently, these assumptions have been weakened for some estimates using the less restrictive notion of regularity index. However, the particular definition of this index makes it unusable for many estimates. In this paper, we define a more general regularity concept: the $r$-regularity. This concept is used to obtain asymptotic law of the histogram without hypothesis on the continuity of the underlying density. As expected, when it does exist, the limit distribution is a standard Gaussian. Then, to illustrate the new definition of $r$-regularity, examples are studied.
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