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October 1997 On the relationship between two asymptotic expansions for the distribution of sample mean and its applications
Rick Routledge, Min Tsao
Ann. Statist. 25(5): 2200-2209 (October 1997). DOI: 10.1214/aos/1069362394

Abstract

Although the cumulative distribution function may be differentiated to obtain the corresponding density function, whether or not a similar relationship exists between their asymptotic expansions remains a question. We provide a rigorous argument to prove that Lugannani and Rice's asymptotic expansion for the cumulative distribution function of the mean of a sample of i.i.d. observations may be differentiated to obtain Daniels's asymptotic expansion for the corresponding density function. We then apply this result to study the relationship between the truncated versions of the two series, which establishes the derivative of a truncated Lugannani and Rice series as an alternative asymptotic approximation for the density function. This alternative approximation in general does not need to be renormalized. Numerical examples demonstrating its accuracy are included.

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Rick Routledge. Min Tsao. "On the relationship between two asymptotic expansions for the distribution of sample mean and its applications." Ann. Statist. 25 (5) 2200 - 2209, October 1997. https://doi.org/10.1214/aos/1069362394

Information

Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0942.62022
MathSciNet: MR1474090
Digital Object Identifier: 10.1214/aos/1069362394

Subjects:
Primary: 62E20
Secondary: 41A60

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 5 • October 1997
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