Bootstrap method for central and intermediate order statistics under power normalization

Haroon Mohamed Barakat; E. M. Nigm; O. M. Khaled

Kybernetika (2015)

  • Volume: 51, Issue: 6, page 923-932
  • ISSN: 0023-5954

Abstract

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It has been known for a long time that for bootstrapping the distribution of the extremes under the traditional linear normalization of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. In this paper, we show that the same is true if we use the bootstrap for estimating a central, or an intermediate quantile under power normalization. A simulation study illustrates and corroborates theoretical results.

How to cite

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Barakat, Haroon Mohamed, Nigm, E. M., and Khaled, O. M.. "Bootstrap method for central and intermediate order statistics under power normalization." Kybernetika 51.6 (2015): 923-932. <http://eudml.org/doc/276248>.

@article{Barakat2015,
abstract = {It has been known for a long time that for bootstrapping the distribution of the extremes under the traditional linear normalization of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. In this paper, we show that the same is true if we use the bootstrap for estimating a central, or an intermediate quantile under power normalization. A simulation study illustrates and corroborates theoretical results.},
author = {Barakat, Haroon Mohamed, Nigm, E. M., Khaled, O. M.},
journal = {Kybernetika},
keywords = {bootstrap technique; power normalization; weak consistency; central order statistics; intermediate order statistics},
language = {eng},
number = {6},
pages = {923-932},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bootstrap method for central and intermediate order statistics under power normalization},
url = {http://eudml.org/doc/276248},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Barakat, Haroon Mohamed
AU - Nigm, E. M.
AU - Khaled, O. M.
TI - Bootstrap method for central and intermediate order statistics under power normalization
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 6
SP - 923
EP - 932
AB - It has been known for a long time that for bootstrapping the distribution of the extremes under the traditional linear normalization of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. In this paper, we show that the same is true if we use the bootstrap for estimating a central, or an intermediate quantile under power normalization. A simulation study illustrates and corroborates theoretical results.
LA - eng
KW - bootstrap technique; power normalization; weak consistency; central order statistics; intermediate order statistics
UR - http://eudml.org/doc/276248
ER -

References

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  1. Athreya, K. B., Fukuchi, J., Bootstrapping extremes of i.i.d. random variables., In: Conference on Extreme Value Theory and Application, Gaitherburg, Maryland 1993, Vol. 3, pp. 23-29. 
  2. Athreya, K. B., Fukuchi, J., 10.1016/s0378-3758(96)00087-0, J. Statist. Plann. Inf. 58 (1997), 299-320. MR1450018DOI10.1016/s0378-3758(96)00087-0
  3. Barakat, H. M., El-Shandidy, M. A., On general asymptotic behaviour of order statistics with random index., Bull. Malays. Math. Sci. Soc. 27 (2004), 169-183. Zbl1185.60020MR2124771
  4. Barakat, H. M., Omar, A. R., 10.1016/j.jspi.2010.06.031, J. Statist. Plann. Inf. 141 (2011), 524-535. MR2719515DOI10.1016/j.jspi.2010.06.031
  5. Barakat, H. M., Omar, A. R., 10.3103/s1066530711040053, Math. Methods Statist. 20 (2011), 365-377. MR2886642DOI10.3103/s1066530711040053
  6. Barakat, H. M., Nigm, E. M., El-Adll, M. E., 10.1007/s00362-008-0128-1, Statist. Papers 51 (2010), 149-164. Zbl1247.60030MR2556592DOI10.1007/s00362-008-0128-1
  7. Barakat, H. M., Nigm, E. M., Khaled, O. M., 10.1016/j.apm.2013.05.045, Applied Math. Modelling 37 (2013), 10162-10169. MR3125527DOI10.1016/j.apm.2013.05.045
  8. Barakat, H. M., Nigm, E. M., Khaled, O. M., Momenkhan, F. A., 10.1080/03610918.2013.805051, Commun. Statist. Simul. Comput. 44 (2015), 1477-1491. MR3290573DOI10.1080/03610918.2013.805051
  9. Chibisov, D. M., 10.1137/1109021, Theory Probab. Appl. 9 (1964), 142-148. MR0165633DOI10.1137/1109021
  10. Efron, B., 10.1214/aos/1176344552, Ann. Statist. 7 (1979), 1-26. Zbl0406.62024MR0515681DOI10.1214/aos/1176344552
  11. Mohan, N. R., Ravi, S., 10.1137/1137119, Theory Probab. Appl. 37 (1992), 632-643. Zbl0774.60029MR1210055DOI10.1137/1137119
  12. Nigm, E. M., 10.1007/bf02595427, Test 15 (2006), 257-269. Zbl1131.62039MR2278954DOI10.1007/bf02595427
  13. Pancheva, E., 10.1007/bfb0074824, Lecture Notes in Math. 1155 (1984), 284-309. MR0825331DOI10.1007/bfb0074824
  14. Smirnov, N. V., Limit distributions for the terms of a variational series., Amer. Math. Soc. Transl. Ser. 11 (1952), 82-143. MR0047277

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