| Title:
|
A second order approximation for the inverse of the distribution function of the sample mean (English) |
| Author:
|
Arevalillo, Jorge M. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
37 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
[91]-102 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
tail probabilities |
| Keyword:
|
saddlepoint approximations |
| MSC:
|
60F05 |
| MSC:
|
62E15 |
| MSC:
|
62E17 |
| MSC:
|
62G20 |
| MSC:
|
62G32 |
| idZBL:
|
Zbl 1264.62044 |
| idMR:
|
MR1825759 |
| . |
| Date available:
|
2009-09-24T19:37:25Z |
| Last updated:
|
2015-03-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135391 |
| . |
| Reference:
|
[1] Bahadur R. R., Rao R. Ranga: On deviations of the sample mean.Ann. Math. Statist. 31 (1960), 1015–1027 MR 0117775, 10.1214/aoms/1177705674 |
| Reference:
|
[2] Barndorff-Nielsen O. E., Cox D. R.: Asymptotic Techniques for Use in Statistics.Chapman and Hall, London 1989 Zbl 0672.62024, MR 1010226 |
| Reference:
|
[3] Daniels H. E.: Saddlepoint approximations in statistics.Ann. Math. Statist. 25 (1954), 631–649 Zbl 0058.35404, MR 0066602, 10.1214/aoms/1177728652 |
| Reference:
|
[4] Feller W.: An Introduction to Probability Theory and its Applications.Vol. I. Wiley, New York 1968 Zbl 0598.60003, MR 0228020 |
| Reference:
|
[5] Field C. A., Ronchetti E.: A tail area influence function and its application to testing.Comm. Statist. C 4 (1985), 19–41 Zbl 0592.62030, MR 0795262 |
| Reference:
|
[6] García–Pérez A.: Behaviour of sign test and one sample median test against changes in the model.Kybernetika 32 (1996), 159–173 Zbl 0873.62046, MR 1385860 |
| Reference:
|
[7] Jensen J. L.: Saddlepoint Approximations.Oxford University Press, New York 1995 Zbl 0764.62021, MR 1354837 |
| . |
