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Article

Keywords:
change point problem; estimators; linear models
Summary:
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.
References:
[1] Antoch J., Hušková M.: Change point problem. Computational Aspects of Model Choice Antoch J. Physica Verlag, Heidelberg, 1992 11-38. MR 1210549
[2] 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
[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. MR 1210549
[5] Billingsley P.: Convergence of Probability Measures. Wiley New York, 1968. MR 0233396 | Zbl 0944.60003
[6] Brodsky B.E., Darkhovsky B.S.: Nonparametric Methods in Change-Point Problem. Kluwer Academic Press, 1993. MR 1228205
[7] Dümbgen L.: The asymptotic behavior of some nonparametric change-point estimators. Annals of Statistics 19 (1991), 1471-1475. MR 1126333
[8] Gänssler P., Stute W.: Wahrscheinlichtkeitstheorie. Springer Verlag Berlin, 1977. MR 0501219
[9] Gombay E.: Testing for change-points with rank and sign statistics. preprint, 1993. MR 1294803 | Zbl 0812.62053
[10] Gombay E., Horváth L.: Approximations for the time of change and the power function in change-point models statistics. preprint, 1994. MR 1391683
[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). MR 0836966
[13] Levin B., Kline J.: The Cusum test of homogeneity with the application in spontaneous abortion epidemiology. Statist. in Medicine 4 469-488 (1985).
[14] Lombard F.: Rank tests for changepoint problem. Biometrika 74 615-624 (1987). MR 0909366
[15] Siegmund D.: Confidence sets in change-point problems. International Statistical Review 56 (1988), 31-38. MR 0963139 | Zbl 0684.62028
[16] Yao Q.: Tests for change-points with epidemic alternatives. Biometrika 80 179-191 (1993). MR 1225223 | Zbl 0771.62080
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