Minimal sufficiency of order statistics in convex models期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Minimal sufficiency of order statistics in convex models

Authors:	Lutz Mattner

Institution:	Department of Statistics, University of Leeds, Leeds LS2 9JT, United Kingdom

Abstract:	Let $\mathcal{P}$ be a convex and dominated statistical model on the measurable space $(\mathcal{X},\mathcal{A})$ , with $\mathcal{A}$ minimal sufficient, and let $n\in\mathbb{N}$ . Then $\mathcal{A}^{\otimes n}_{\operatorname{sym}}$ , the $\sigma$ -algebra of all permutation invariant sets belonging to the -fold product $\sigma$ -algebra $\mathcal{A}^{\otimes n}$ , is shown to be minimal sufficient for the corresponding model for independent observations, $\mathcal{P}^n = \left\{P^{\otimes n}:P\in\mathcal{P}\right\}$ . The main technical tool provided and used is a functional analogue of a theorem of Grzegorek (1982) concerning generators of $\mathcal{A}^{\otimes n}_{\operatorname{sym}}$ .

Keywords:	Comparison of $\sigma$-algebras nonparametric models permutation invariance symmetric sets

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文