The Annals of Probability

Approximation of Product Measures with an Application to Order Statistics

R.-D. Reiss

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Abstract

Firstly, a well-known upper estimate concerning the distance of independent products of probability measures is extended to the case of signed measures. The upper bound depends on the total variation of the signed measures and on the distances of the single components where the distances are measured in the sup-metric. Under certain regularity conditions, the upper estimate can be sharpened by using asymptotic expansions. These expansions hold true over the set of all integrable function. An application of these results together with an asymptotic expansion of the distribution of a single order statistic yields an asymptotic expansion of the joint distribution of order statistics under the exponential distribution.

Article information

Source
Ann. Probab., Volume 9, Number 2 (1981), 335-341.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994477

Digital Object Identifier
doi:10.1214/aop/1176994477

Mathematical Reviews number (MathSciNet)
MR606998

Zentralblatt MATH identifier
0462.60037

JSTOR
links.jstor.org

Subjects
Primary: 60F99: None of the above, but in this section
Secondary: 62E15: Exact distribution theory 62G30: Order statistics; empirical distribution functions

Keywords
Independent product measure distance of measures asymptotic expansion joint distribution of order statistics

Citation

Reiss, R.-D. Approximation of Product Measures with an Application to Order Statistics. Ann. Probab. 9 (1981), no. 2, 335--341. doi:10.1214/aop/1176994477. https://projecteuclid.org/euclid.aop/1176994477


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