Bayesian statistical inference for sampling a finite population
type: Item
instance of: scholarly article
title: Bayesian statistical inference for sampling a finite population
zbMATH Open document ID: 0608.62036
author: Albert Y. Lo
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: \textit{W. A. Ericson} [J. R. Stat. Soc., Ser. B 31, 195-233 (1969; Zbl 0186.519)] and \textit{B. Hoadley} [J. Am. Stat. Assoc. 64, 216-229 (1969; Zbl 0177.223)] showed that if the prior distribution of the number of population variables belonging to the j th category is Dirichlet- multinomial, the posterior distribution of unobserved population variables (given the observed ones) belonging to each category is also of the same type. \textit{A. Scott} [Ann. Math. Stat. 42, 1113-1117 (1971; Zbl 0228.62007)] proved that the centered and rescaled posterior distribution converges to that of a normal random vector for arbitrary priors. In the present paper these results are extended to the case of arbitrary population variables. The author defines the Dirichlet-multinomial process, extends the Ericson-Hoadley theorem and shows that the Dirichlet process is the limit of the Dirichlet-multinomial process. Next, it is proved that the large-sample posterior distribution of the population empirical distribution, centered and rescaled, is a Brownian bridge with a change of time scale. As corollaries, the large-sample Bayes confidence band for the population empirical distribution function and the large- sample Bayes confidence interval for the population mean are obtained.
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62F25
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 3984324
zbMATH Keywords: sampling a finite population
zbMATH Keywords: prior distribution
zbMATH Keywords: Dirichlet-multinomial
zbMATH Keywords: centered and rescaled posterior distribution
zbMATH Keywords: Ericson-Hoadley theorem
zbMATH Keywords: Dirichlet process
zbMATH Keywords: large-sample posterior distribution
zbMATH Keywords: Brownian bridge
zbMATH Keywords: large-sample Bayes confidence band
zbMATH Keywords: empirical distribution
zbMATH Keywords: Bayes confidence interval
zbMATH Keywords: population mean
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350061
OpenAlex ID: W2089980968
DOI: 10.1214/AOS/1176350061
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description: scientific article; zbMATH DE number 3984324