Kybernetika 47 no. 6, 866-879, 2011

Detection of transient change in mean - a linear behavior inside epidemic interval

Daniela Jarušková


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.


detection of transient change, trimmed maximum-type test statistic, extremes of Gaussian fields


62F05, 60G60, 60G70


  1. J. Antoch and M. Hušková: Tests and estimators for epidemic alternatives. Tatra Mountains Math. Publ. 7 (1996), 311-329.   CrossRef
  2. J. Bai and P. Perron: Estimating and testing linear models with multiple structural changes. Econometrica 66 (1998), 47-78.   CrossRef
  3. P. J. Bickel and M. J. Wichura: Covergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Statist. 42 (1971), 1656-1670.   CrossRef
  4. H. P. Chan and T. L. Lai: 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.   CrossRef
  5. M. Csörgő and L. Horváth: Limit Theorems in Change Point Analysis. J. Wiley, New York 1997.   CrossRef
  6. P. I. Feder: On asymptotic distribution theory in segmented regression problems - identified case. Ann. Statist. 3 (1975), 49-83.   CrossRef
  7. M. Hušková: Estimators for epidemic alternatives. Comment. Math. Univ. Carolinae 36 (1995), 279-291.   CrossRef
  8. D. Jarušková and V. I. Piterbarg: Log-likelihood ratio test for detecting transient change. Statist. Probab. Lett. 81 (2011), 552-559.   CrossRef
  9. Z. Kabluchko: Extreme-value analysis of standardized Gaussian increaments. Not published preprint. ArXiv:0706.1849v3[math.PR] (2008).   CrossRef
  10. B. Levin and J. Kline: The cusum test of homogeneity with an application to spontaneous abortion epidemiology. Statist. in Medicine 4 (1985), 469-488.   CrossRef
  11. C. R. Loader: Large - deviation approximations to the distribution of scan statistics. Adv. Appl. Prob. 23 (1991), 751-771.   CrossRef
  12. V. I. Piterbarg: Asymptotic methods in the theory of Gaussian processes and fields. Translations of Mathematical Monographs, vol. 148.} \newblock{Amer. Math. Soc. (1996), Providence.   CrossRef
  13. D. Siegmund: Approximate tail probabilities for the maxima of some random fields. Ann. Probab. 16 (1988), 487-501.   CrossRef
  14. D. Siegmund and E. S. Venkatranan: Using the generalized likelihood ratio statistic for sequential detection of change-point. Ann. Statist. 23 (1995), 255-271.   CrossRef
  15. D. Siegmund and B. Yakir: Tail probabilities for the null distribution of scanning statistics. Bernoulli 6 (2000), 191-213.   CrossRef