Minimax estimation under convex loss when the parameter interval is bounded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

Minimax estimation under convex loss when the parameter interval is bounded

Authors:	Dr. J. Eichenauer-Herrmann Prof. Dr. W. Fieger

Affiliation:	1. Technische Hochschule Darmstadt, Fachbereich Mathematik, Arbeitsgruppe Stochastik und Operations Research, Schlo?gartenstr. 7, D-6100, Darmstadt, FRG 2. Fakult?t für Mathematik, Institut für Mathematische Statistik, Universit?t Karlsruhe, Englerstr. 2, D-7500, Karlsruhe 1, FRG

Abstract:	In the present paper families of truncated distributions with a Lebesgue density $f(theta ,x) = C_n (theta )left( {prodlimits_{i = 1}^n {f_0 (x_i )} } right)I_{left[ {theta ,theta + 1} right]^n } (x)$ forx=(x ₁,...,x _n) ε ℝⁿ are considered, wheref ₀:ℝ → (0, ∞) is a known continuous function andC _n(ϑ) denotes a normalization constant. The unknown truncation parameterϑ which is assumed to belong to a bounded parameter intervalΘ=[0,d] is to be estimated under a convex loss function. It is studied whether a two point prior and a corresponding Bayes estimator form a saddle point when the parameter interval is sufficiently small.

Keywords:	Minimax estimation bounded parameter interval family of truncated distributions uniform distribution convex loss function least favourable two point prior
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