Construction of minimax tests for bounded families of probability densities
type: Item
instance of: scholarly article
title: Construction of minimax tests for bounded families of probability densities
zbMATH Open document ID: 0798.62056
DOI: 10.1007/BF02613659
author: Robert Hafner
published in: Metrika
publication date: 1993-05-16T00:00:00Z
full work available at URL: https://eudml.org/doc/176442
review text: Let \(f\) denote the Radon-Nikodym density of a probability measure with respect to a \(\sigma\)-finite measure \(\mu\) and let \(\underline f, {\underset {=} f}, \underline g, {\underset {=} g}\) be nonnegative, measurable functions satisfying \[ \oint \underline f d \mu \leq 1 \leq \oint {\underset {=} f} d \mu \quad \text{and} \quad \oint \underline g d \mu \leq 1 \leq \oint {\underset {=} g} d \mu. \] The compound test problem under consideration, \[ H_ 0 : \underline f \leq f \leq {\underset {=} f} \text{ vs. } H_ 1 : \underline g \leq g \leq {\underset {=} g}, \] is dealt with by using the Neyman-Pearson theory for single hypotheses and the risk-function method. Least favourable pairs of distributions are constructed as well as a family of minimax tests.
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62C20
zbMATH DE Number: 168604
zbMATH Keywords: least favourable pairs of distributions
zbMATH Keywords: Radon-Nikodym density
zbMATH Keywords: compound test problem
zbMATH Keywords: Neyman-Pearson theory for single hypotheses
zbMATH Keywords: risk-function method
zbMATH Keywords: minimax tests
reviewed by: Wolf-Dieter Richter
MaRDI profile type: Publication
cites work: Minimax Tests for Bounded Families of Distribution Densities
cites work: On the construction of least favourable pairs of distributions
cites work: Construction of least favourable pairs of distributions and of eobnst tests for contamination neighbourhoods
cites work: Simple construction of least favourable pairs of distributions and of robust tests for prokhorov-neighbourhoods
cites work: Q3774700
cites work: Minimax tests and the Neyman-Pearson lemma for capacities
cites work: The fundamental Neyman‐Pearson lemma and the Radon‐Nikodym theorem from a common statistical point of view
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description: scientific article; zbMATH DE number 168604