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Characterizations of non-normalized discrete probability distributions and their application in statistics
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In this article, the authors derive explicit formulae for the mass functions of discrete probability laws that identify those distributions and apply these identities to develop tools for the solution of statistical problems.Abstract:
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop tools for the solution of statistical problems. Our characterizations, and hence the applications built on them, do not require any knowledge about normalization constants of the probability laws. We discuss several examples where this lack of feasibility of the normalization constant is a built-in feature. To demonstrate that our statistical methods are sound, we provide comparative simulation studies for the testing of fit to the Poisson distribution and for parameter estimation of the negative binomial family when both parameters are unknown. We also consider the problem of parameter estimation for discrete exponential-polynomial models which generally are non-normalized.read more
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Stein’s Method Meets Computational Statistics: A Review of Some Recent Developments
TL;DR: In this article , a survey of recent developments in the field of Stein's method and statistics is presented, including tools to benchmark and compare sampling methods such as approximate Markov chain Monte Carlo, deterministic alternatives to sampling methods, control variate techniques, parameter estimation and goodness-of-fit testing.
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Goodness-of-fit tests for Poisson count time series based on the Stein–Chen identity
Posted Content
Stein's Method Meets Statistics: A Review of Some Recent Developments
Andreas Anastasiou,Alessandro Barp,François-Xavier Briol,Bruno Ebner,Robert E. Gaunt,Fatemeh Ghaderinezhad,Jackson Gorham,Arthur Gretton,Christophe Ley,Qiang Liu,Lester Mackey,Chris J. Oates,Gesine Reinert,Yvik Swan +13 more
TL;DR: In this paper, the authors present a survey of recent developments in theoretical statistics as well as in computational statistics and stimulate further research into the successful field of Stein's method and statistics, including explicit error bounds for asymptotic approximations of estimators and test statistics, tools to benchmark and compare sampling methods such as approximate Markov chain Monte Carlo, deterministic alternatives to sampling methods, control variate techniques, and goodness-of-fit testing.
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Anscombe's tests of fit for the negative binomial distribution
TL;DR: In this article, the authors re-examine tests of fit for the negative binomial distribution that were introduced by Anscombe (1950); they are based on a dispersion statistic U and a third moment statistic T. Small sample power calculations are given for U and T.
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Univariate Discrete Distributions
TL;DR: In this paper, the authors propose a family of Discrete Distributions, which includes Hypergeometric, Mixture, and Stopped-Sum Distributions (see Section 2.1).