The Annals of Statistics

Deficiency distance between multinomial and multivariate normal experiments

Andrew V. Carter

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Abstract

The deficiency distance between a multinomial and a multivariate normal experiment is bounded under a condition that the parameters are bounded away from zero. This result can be used as a key step in establishing asymptotic normal approximations to nonparametric density estimation experiments. The bound relies on the recursive construction of explicit Markov kernels that can be used to reproduce one experiment from the other. The distance is then bounded using classic local-limit bounds between binomial and normal distributions. Some extensions to other appropriate normal experiments are also presented.

Article information

Source
Ann. Statist., Volume 30, Number 3 (2002), 708-730.

Dates
First available in Project Euclid: 6 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1028674839

Digital Object Identifier
doi:10.1214/aos/1028674839

Mathematical Reviews number (MathSciNet)
MR1922539

Zentralblatt MATH identifier
1029.62005

Subjects
Primary: 62B15: Theory of statistical experiments
Secondary: 62G20: Asymptotic properties 62G07: Density estimation

Keywords
Deficiency distance nonparametric experiments density estimation multinomial distribution

Citation

Carter, Andrew V. Deficiency distance between multinomial and multivariate normal experiments. Ann. Statist. 30 (2002), no. 3, 708--730. doi:10.1214/aos/1028674839. https://projecteuclid.org/euclid.aos/1028674839


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