研究者情報 | 神奈川大学

カナザワ　ユウイチロウ Kanazawa Yuichiro 金澤　雄一郎所属神奈川大学経済学部経済学科/現代ビジネス学科職種教授
言語種別	英語
発行・発表の年月	1992/03
形態種別	学術雑誌
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	ANNALS OF STATISTICS
出版社・発行元	INST MATHEMATICAL STATISTICS
巻・号・頁	20(1),pp.291-304
著者・共著者	Y KANAZAWA
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 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 n^(1/3) 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
ISSN	00905364