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2021 Discrete mixture representations of parametric distribution families: Geometry and statistics
Ludwig Baringhaus, Rudolf Grübel
Electron. J. Statist. 15(1): 37-70 (2021). DOI: 10.1214/20-EJS1795

Abstract

We investigate existence and properties of discrete mixture representations $P_{\theta }=\sum _{i\in E}w_{\theta }(i)\,Q_{i}$ for a given family $P_{\theta }$, $\theta \in \Theta $, of probability measures. The noncentral chi-squared distributions provide a classical example. We obtain existence results and results about geometric and statistical aspects of the problem, the latter including loss of Fisher information, Rao-Blackwellization, asymptotic efficiency and nonparametric maximum likelihood estimation of the mixing probabilities.

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Ludwig Baringhaus. Rudolf Grübel. "Discrete mixture representations of parametric distribution families: Geometry and statistics." Electron. J. Statist. 15 (1) 37 - 70, 2021. https://doi.org/10.1214/20-EJS1795

Information

Received: 1 April 2020; Published: 2021
First available in Project Euclid: 6 January 2021

Digital Object Identifier: 10.1214/20-EJS1795

Subjects:
Primary: 60E05
Secondary: 62G05

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Vol.15 • No. 1 • 2021
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