Distributional Inference

A.H. Kroese, E.A. van der Meulen, Klaas Poortema, W. Schaafsma

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    Abstract

    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 nondogmatic approach.
    Original languageEnglish
    Pages (from-to)63-82
    Number of pages20
    JournalStatistica Neerlandica
    Volume49
    Issue number1
    DOIs
    Publication statusPublished - 1995

    Keywords

    • Decision theory
    • Foundations
    • Fiducial inference
    • Unbiasedness
    • Invariance

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  • Cite this

    Kroese, A. H., van der Meulen, E. A., Poortema, K., & Schaafsma, W. (1995). Distributional Inference. Statistica Neerlandica, 49(1), 63-82. https://doi.org/10.1111/j.1467-9574.1995.tb01455.x