Distributional inference
作者:
A. H. Kroese,
E. A. Meulen,
K. Poortema,
W. Schaafsma,
期刊:
Statistica Neerlandica
(WILEY Available online 1995)
卷期:
Volume 49,
issue 1
页码: 63-82
ISSN:0039-0402
年代: 1995
DOI:10.1111/j.1467-9574.1995.tb01455.x
出版商: Blackwell Publishing Ltd
关键词: decision theory;fiducial inference;foundations;invariance;unbiasedness
数据来源: WILEY
摘要:
The making of statistical inferences in distributional form is conceptionally complicated because the epistemic ‘probabilities’ assigned are mixtures of fact and fiction. In this respect they are essentially different from ‘physical’ or ‘frequency‐theoretic’ probabilities. The distributional form is so attractive and useful, however, that it should be pursued. Our approach is In line with Walds theory of statistical decision functions and with Lehmann's books about hypothesis testing and point estimation: loss functions are defined, risk functions are studied, unbiasedness and equivariance restrictions are made, etc. A central theme is that the loss function should be ‘proper’. This fundamental concept has been explored by meteorologists, psychometrists, Bayesian statisticians, and others. The paper should be regarded as an attempt to reconcile various schools of statisticians. By accepting what we regard 88 good and useful in the various approaches we are trying to develop a non
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