カナザワ,ユウイチロウ   KANAZAWA, Yuichiro
  金澤 雄一郎
   所属   国際基督教大学教養学部 アーツ・サイエンス学科
   職種   教授
言語種別 英語
発行・発表の年月 1992
形態種別 研究論文
査読 査読あり
標題 An Optimal Variable Cell Histogram Based on the Sample Spacings
執筆形態 単著
掲載誌名 The Annals of Statistics
掲載区分国外
巻・号・頁 20(1),pp.291-304
概要 Suppose we wish to construct a variable k-cell histogram based on an independent identically distributed sample of size n−1 from an unknown density f on the interval of finite length. A variable cell histogram requires cutpoints and heights of all of its cells to be specified. We propose the following procedure: (i) choose from the order statistics corresponding to the sample a set of k+1 cutpoints that maximize a criterion, a function of the sample spacings; (ii) compute heights of the k cells according to a formula. The resulting histogram estimates a k-cell theoretical histogram that stays constant within a cell and that minimizes the Hellinger distance to the density f. The histogram tends to estimate low density regions accurately and is easy to compute. We find the number of cells of order n1/3 minimizes the mean Hellinger distance between the density f and a class of histograms whose cutpoints are chosen from the order statistics.
DOI doi:10.1214/aos/1176348523