Open Access
June 2002 Deficiency distance between multinomial and multivariate normal experiments
Andrew V. Carter
Ann. Statist. 30(3): 708-730 (June 2002). DOI: 10.1214/aos/1028674839


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.


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Andrew V. Carter. "Deficiency distance between multinomial and multivariate normal experiments." Ann. Statist. 30 (3) 708 - 730, June 2002.


Published: June 2002
First available in Project Euclid: 6 August 2002

zbMATH: 1029.62005
MathSciNet: MR1922539
Digital Object Identifier: 10.1214/aos/1028674839

Primary: 62B15
Secondary: 62G07 , 62G20

Keywords: deficiency distance , Density estimation , multinomial distribution , Nonparametric experiments

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 3 • June 2002
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