Estimators for epidemic alternatives

Marie Hušková

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 2, page 279-291
  • ISSN: 0010-2628

Abstract

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We introduce and study the behavior of estimators of changes in the mean value of a sequence of independent random variables in the case of so called epidemic alternatives which is one of the variants of the change point problem. The consistency and the limit distribution of the estimators developed for this situation are shown. Moreover, the classical estimators used for `at most change' are examined for the studied situation.

How to cite

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Hušková, Marie. "Estimators for epidemic alternatives." Commentationes Mathematicae Universitatis Carolinae 36.2 (1995): 279-291. <http://eudml.org/doc/247736>.

@article{Hušková1995,
abstract = {We introduce and study the behavior of estimators of changes in the mean value of a sequence of independent random variables in the case of so called epidemic alternatives which is one of the variants of the change point problem. The consistency and the limit distribution of the estimators developed for this situation are shown. Moreover, the classical estimators used for `at most change' are examined for the studied situation.},
author = {Hušková, Marie},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {change point problem; estimators; linear models; linear models; changes in mean value; epidemic alternatives; change point problem; consistency; limit distribution},
language = {eng},
number = {2},
pages = {279-291},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Estimators for epidemic alternatives},
url = {http://eudml.org/doc/247736},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Hušková, Marie
TI - Estimators for epidemic alternatives
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 2
SP - 279
EP - 291
AB - We introduce and study the behavior of estimators of changes in the mean value of a sequence of independent random variables in the case of so called epidemic alternatives which is one of the variants of the change point problem. The consistency and the limit distribution of the estimators developed for this situation are shown. Moreover, the classical estimators used for `at most change' are examined for the studied situation.
LA - eng
KW - change point problem; estimators; linear models; linear models; changes in mean value; epidemic alternatives; change point problem; consistency; limit distribution
UR - http://eudml.org/doc/247736
ER -

References

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  1. Antoch J., Hušková M., Change point problem, Computational Aspects of Model Choice Antoch J. Physica Verlag, Heidelberg, 1992 11-38. MR1210549
  2. Antoch J., Hušková M., Procedures for the detection of multiple changes in series of independent observations, Proceedings of the Prague Symposium on Asymptotic Statistics Hušková M. and Mandl P. Physica Verlag, Heidelberg, 1994 3-20. MR1311925
  3. Antoch J., Hušková M., Tests and estimators for epidemic alternatives, submitted, 1994. 
  4. Antoch J., Hušková M., Veraverbeke N., Change-point problem and bootstrap, submitted, 1993. MR1210549
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  6. Brodsky B.E., Darkhovsky B.S., Nonparametric Methods in Change-Point Problem, Kluwer Academic Press, 1993. MR1228205
  7. Dümbgen L., The asymptotic behavior of some nonparametric change-point estimators, Annals of Statistics 19 (1991), 1471-1475. (1991) MR1126333
  8. Gänssler P., Stute W., Wahrscheinlichtkeitstheorie, Springer Verlag Berlin, 1977. MR0501219
  9. Gombay E., Testing for change-points with rank and sign statistics, preprint, 1993. Zbl0812.62053MR1294803
  10. Gombay E., Horváth L., Approximations for the time of change and the power function in change-point models statistics, preprint, 1994. MR1391683
  11. Horváth L., Some applications of the likelihood method in change-point models statistics, Transactions of the Twelfth Prague Conference, 1994, pp. 106-108. 
  12. Khakhubia T.G., A limit theorem for a maximum likelihood estimate of the disorder time, Theory Prob. Appl. 31 141-144 (1986). (1986) MR0836966
  13. Levin B., Kline J., The Cusum test of homogeneity with the application in spontaneous abortion epidemiology, Statist. in Medicine 4 469-488 (1985). (1985) 
  14. Lombard F., Rank tests for changepoint problem, Biometrika 74 615-624 (1987). (1987) MR0909366
  15. Siegmund D., Confidence sets in change-point problems, International Statistical Review 56 (1988), 31-38. (1988) Zbl0684.62028MR0963139
  16. Yao Q., Tests for change-points with epidemic alternatives, Biometrika 80 179-191 (1993). (1993) Zbl0771.62080MR1225223

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