Previous |  Up |  Next

Article

Keywords:
detection of transient change; trimmed maximum-type test statistic; extremes of Gaussian fields
Summary:
A procedure for testing occurrance of a transient change in mean of a sequence is suggested where inside an epidemic interval the mean is a linear function of time points. Asymptotic behavior of considered trimmed maximum-type test statistics is presented. Approximate critical values are obtained using an approximation of exceedance probabilities over a high level by Gaussian fields with a locally stationary structure.
References:
[1] Antoch, J., Hušková, M.: Tests and estimators for epidemic alternatives. Tatra Mountains Math. Publ. 7 (1996), 311–329. MR 1408487
[2] Bai, J., Perron, P.: Estimating and testing linear models with multiple structural changes. Econometrica 66 (1998), 47–78. DOI 10.2307/2998540 | MR 1616121 | Zbl 1056.62523
[3] Bickel, P. J., Wichura, M. J.: Covergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Statist. 42 (1971), 1656–1670. DOI 10.1214/aoms/1177693164 | MR 0383482
[4] Chan, H. P., Lai, T. L.: Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices. Ann. Probab. 34 (2006), 80–121. DOI 10.1214/009117905000000378 | MR 2206343 | Zbl 1106.60022
[5] Csörgő, M., Horváth, L.: Limit Theorems in Change Point Analysis. J. Wiley, New York 1997. MR 2743035
[6] Feder, P. I.: On asymptotic distribution theory in segmented regression problems – identified case. Ann. Statist. 3 (1975), 49–83. DOI 10.1214/aos/1176342999 | MR 0378267 | Zbl 0324.62014
[7] Hušková, M.: Estimators for epidemic alternatives. Comment. Math. Univ. Carolinae 36 (1995), 279–291. MR 1357530
[8] Jarušková, D., Piterbarg, V. I.: Log-likelihood ratio test for detecting transient change. Statist. Probab. Lett. 81 (2011), 552–559. DOI 10.1016/j.spl.2011.01.006 | MR 2772911 | Zbl 1209.62141
[9] Kabluchko, Z.: Extreme-value analysis of standardized Gaussian increaments. Not published preprint. ArXiv:0706.1849v3[math.PR] (2008).
[10] Levin, B., Kline, J.: The cusum test of homogeneity with an application to spontaneous abortion epidemiology. Statist. in Medicine 4 (1985), 469–488. DOI 10.1002/sim.4780040408
[11] Loader, C. R.: Large – deviation approximations to the distribution of scan statistics. Adv. Appl. Prob. 23 (1991), 751–771. DOI 10.2307/1427674 | MR 1133726 | Zbl 0741.60036
[12] Piterbarg, V. I.: Asymptotic methods in the theory of Gaussian processes and fields. Translations of Mathematical Monographs, vol. 148. Amer. Math. Soc. (1996), Providence. MR 1361884 | Zbl 0841.60024
[13] Siegmund, D.: Approximate tail probabilities for the maxima of some random fields. Ann. Probab. 16 (1988), 487–501. DOI 10.1214/aop/1176991769 | MR 0929059 | Zbl 0646.60032
[14] Siegmund, D., Venkatranan, E. S.: Using the generalized likelihood ratio statistic for sequential detection of change-point. Ann. Statist. 23 (1995), 255–271. DOI 10.1214/aos/1176324466 | MR 1331667
[15] Siegmund, D., Yakir, B.: Tail probabilities for the null distribution of scanning statistics. Bernoulli 6 (2000), 191–213. DOI 10.2307/3318574 | MR 1748719 | Zbl 0976.62048
Partner of
EuDML logo