Abstract
We discuss the asymptotic properties of some tests to detect possible changes in the mean of linear processes.
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References
Bai, J. (1994). Least squares estimation of a shift in linear processes, J. Time Ser. Anal., 15, 453–472.
Csörgő, M. and Horváth, L. (1988). Nonparametric methods for change-point problems, Handbook of Statistics, 7, 275–280.
Csörgő, M. and Horváth, L. (1993). Weighted Approximations in Probability and Statistics, Wiley, New York.
Csörgő, M. and Révész, P. (1981). Strong Approximations in Probability and Statistics, Academic Press, New York.
Darling, D. A. and Erdős, P. (1956). A limit theorem for maximum of normalized sums of independent random variables, Duke Math. J., 23, 143–155.
Davis, R. A., Huang, D. and Yao, Y. C. (1995). Testing for a change in the parameter values and order of an autoregressive model, Ann. Statist., 23, 283–304.
Giraitis, L. and Leipus, R. (1990). A functional CLT for nonparametric estimates of spectra and change-point problem for spectral function, Lietuvos Matematikos Rinkinys, 30, 674–697.
Giraitis, L. and Leipus, R. (1992). Testing and estimating in the change-point problem of the spectral function, Lietuvos Matematikos Rinkinys, 32, 20–38.
Gombay, E. and Horváth, L. (1990). Asymptotic distributions of maximum likelihood tests for change in the mean, Biometrika, 77, 411–414.
Gombay, E. and Horváth, L. (1994). An application of the maximum likelihood test to the change-point problem, Stochastic Process. Appl., 50, 161–171.
Gorodetskii, V. V. (1977). On the strong mixing property for linear sequences, Theory Probab. Appl., 22, 411–413.
Haccou, P., Meelis, E. and Van de Geer, S. (1988). The likelihood ratio test for the change point problem for exponentially distributed random variables, Stochastic Process. Appl., 27, 121–139.
Horváth, L. (1993a). Change in autoregressive processes, Stochastic Process. Appl., 44, 221–242.
Horváth, L. (1993b). The maximum likelihood method for testing changes in the parameters of normal observations, Ann. Statist., 21, 671–680.
Horváth, L. and Kokoszka, P. (1995). The effect of long-range dependence on change-point estimators (preprint).
Ibragimov, I. A. and Linnik, Y. V. (1971). Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen.
Kuelbs, J. and Philipp, W. (1980). Almost sure invariance principles for partial sums of mixing B-valued random variables, Ann. Probab., 8, 1003–1036.
Kulpelger, R. J. (1985). On the residuals of autoregressive processes and polynomial regression, Stochastic Process. Appl., 21, 107–118.
Page, E. S. (1954). Continuous inspection schemes, Biometrika, 41, 100–105.
Page, E. S. (1955). A test for change in a parameter occurring at an unknown point, Biometrika, 42, 523–526.
Philipp, W. and Stout, W. (1975). Almost sure invariance principles for partial sums of weakly dependent random variables, Mem. Amer. Math. Soc., 161, 1–137.
Picard, D. (1985). Testing and estimating change-points in time series, Adv. in Appl. Probab., 17, 841–867.
Sen, A. and Srivastava, M. S. (1975a). On tests for detecting change in the mean, Ann. Statist., 3, 98–108.
Son, A. and Srivastava, M. S. (1975b). Some one-sided tests for change in level, Technometrics, 17, 61–64.
Shorack, G. R. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics, Wiley, New York.
Tang, S. M. and MacNeill, I. B. (1993). The effect of serial correlation on tests for parameter change at unknown time, Ann. Statist., 21, 552–575.
Withers, C. S. (1981). Conditions for linear processes to be strong-mixing, Zeit. Wahrscheinlichkeitsth., 57, 477–480.
Worsley, K. J. (1979). On the likelihood ratio test for a shift in location of normal populations, J. Amer. Statist. Assoc., 74, 365–367.
Worsley, K. J. (1986). Confidence regions and tests for a change-point in a sequence of exponential random variables, Biometrika, 73, 91–104.
Yao, Y. C. and Davis, R. A. (1986). The asymptotic behavior of the likelihood ratio statistic for testing a shift in mean in a sequence of independent normal variates, Sankhyā Ser. A, 48, 339–353.
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Horváth, L. Detection of Changes in Linear Sequences. Annals of the Institute of Statistical Mathematics 49, 271–283 (1997). https://doi.org/10.1023/A:1003110912735
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DOI: https://doi.org/10.1023/A:1003110912735