A second order approximation for the inverse of the distribution function of the sample mean

Jorge M. Arevalillo

Kybernetika (2001)

  • Volume: 37, Issue: 1, page [91]-102
  • ISSN: 0023-5954

Abstract

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The classical quantile approximation for the sample mean, based on the central limit theorem, has been proved to fail when the sample size is small and we approach the tail of the distribution. In this paper we will develop a second order approximation formula for the quantile which improves the classical one under heavy tails underlying distributions, and performs very accurately in the upper tail of the distribution even for relatively small samples.

How to cite

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Arevalillo, Jorge M.. "A second order approximation for the inverse of the distribution function of the sample mean." Kybernetika 37.1 (2001): [91]-102. <http://eudml.org/doc/33519>.

@article{Arevalillo2001,
abstract = {The classical quantile approximation for the sample mean, based on the central limit theorem, has been proved to fail when the sample size is small and we approach the tail of the distribution. In this paper we will develop a second order approximation formula for the quantile which improves the classical one under heavy tails underlying distributions, and performs very accurately in the upper tail of the distribution even for relatively small samples.},
author = {Arevalillo, Jorge M.},
journal = {Kybernetika},
keywords = {tail probabilities; saddlepoint approximations; tail probabilities; saddlepoint approximations},
language = {eng},
number = {1},
pages = {[91]-102},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A second order approximation for the inverse of the distribution function of the sample mean},
url = {http://eudml.org/doc/33519},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Arevalillo, Jorge M.
TI - A second order approximation for the inverse of the distribution function of the sample mean
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 1
SP - [91]
EP - 102
AB - The classical quantile approximation for the sample mean, based on the central limit theorem, has been proved to fail when the sample size is small and we approach the tail of the distribution. In this paper we will develop a second order approximation formula for the quantile which improves the classical one under heavy tails underlying distributions, and performs very accurately in the upper tail of the distribution even for relatively small samples.
LA - eng
KW - tail probabilities; saddlepoint approximations; tail probabilities; saddlepoint approximations
UR - http://eudml.org/doc/33519
ER -

References

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  2. Barndorff-Nielsen O. E., Cox D. R., Asymptotic Techniques for Use in Statistics, Chapman and Hall, London 1989 Zbl0672.62024MR1010226
  3. Daniels H. E., 10.1214/aoms/1177728652, Ann. Math. Statist. 25 (1954), 631–649 (1954) Zbl0058.35404MR0066602DOI10.1214/aoms/1177728652
  4. Feller W., An Introduction to Probability Theory and its Applications, Vol. I. Wiley, New York 1968 Zbl0598.60003MR0228020
  5. Field C. A., Ronchetti E., A tail area influence function and its application to testing, Comm. Statist. C 4 (1985), 19–41 (1985) Zbl0592.62030MR0795262
  6. García–Pérez A., Behaviour of sign test and one sample median test against changes in the model, Kybernetika 32 (1996), 159–173 (1996) Zbl0873.62046MR1385860
  7. Jensen J. L., Saddlepoint Approximations, Oxford University Press, New York 1995 Zbl0764.62021MR1354837

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