Estimators for epidemic alternatives
Hušková, Marie
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 279-291 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1995-01-01
Classification:  62F05,  62F12,  62G05,  62G20,  62J05
@article{118757,
     author = {Marie Hu\v skov\'a},
     title = {Estimators for epidemic alternatives},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {279-291},
     zbl = {0831.62024},
     mrnumber = {1357530},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118757}
}
Hušková, Marie. Estimators for epidemic alternatives. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 279-291. http://gdmltest.u-ga.fr/item/118757/

Antoch J.; Hušková M. Change point problem, Computational Aspects of Model Choice Antoch J. Physica Verlag, Heidelberg, 1992 11-38. | MR 1210549

Antoch J.; Hušková M. Procedures for the detection of multiple changes in series of independent observations, Proceedings of the $5^{\hskip 1 pt {th}}$ Prague Symposium on Asymptotic Statistics Hušková M. and Mandl P. Physica Verlag, Heidelberg, 1994 3-20. | MR 1311925

Antoch J.; Hušková M. Tests and estimators for epidemic alternatives, submitted, 1994.

Antoch J.; Hušková M.; Veraverbeke N. Change-point problem and bootstrap, submitted, 1993. | MR 1210549

Billingsley P. Convergence of Probability Measures, Wiley New York, 1968. | MR 0233396 | Zbl 0944.60003

Brodsky B.E.; Darkhovsky B.S. Nonparametric Methods in Change-Point Problem, Kluwer Academic Press, 1993. | MR 1228205

Dümbgen L. The asymptotic behavior of some nonparametric change-point estimators, Annals of Statistics 19 (1991), 1471-1475. (1991) | MR 1126333

Gänssler P.; Stute W. Wahrscheinlichtkeitstheorie, Springer Verlag Berlin, 1977. | MR 0501219

Gombay E. Testing for change-points with rank and sign statistics, preprint, 1993. | MR 1294803 | Zbl 0812.62053

Gombay E.; Horváth L. Approximations for the time of change and the power function in change-point models statistics, preprint, 1994. | MR 1391683

Horváth L. Some applications of the likelihood method in change-point models statistics, Transactions of the Twelfth Prague Conference, 1994, pp. 106-108.

Khakhubia T.G. A limit theorem for a maximum likelihood estimate of the disorder time, Theory Prob. Appl. 31 141-144 (1986). (1986) | MR 0836966

Levin B.; Kline J. The Cusum test of homogeneity with the application in spontaneous abortion epidemiology, Statist. in Medicine 4 469-488 (1985). (1985)

Lombard F. Rank tests for changepoint problem, Biometrika 74 615-624 (1987). (1987) | MR 0909366

Siegmund D. Confidence sets in change-point problems, International Statistical Review 56 (1988), 31-38. (1988) | MR 0963139 | Zbl 0684.62028

Yao Q. Tests for change-points with epidemic alternatives, Biometrika 80 179-191 (1993). (1993) | MR 1225223 | Zbl 0771.62080