Asymptotic distribution of the jump change-point estimator

Abstract

The asymptotic distribution of the change-point estimator in a jump changepoint model is considered. For the jump change-point model X _i = a + θI{[nτ ₀] < i ≤ n} + ɛ _i, where ɛ _i (i = 1, ..., n) are independent identically distributed random variables with Eɛ _i = 0 and Var(ɛ _i) < ∞, with the help of the slip window method, the asymptotic distribution of the jump change-point estimator $\hat \tau$ is studied under the condition of the local alternative hypothesis.

Keywords

Change-point / Local alternative hypothesis / Asymptotic distribution

References

[1] Aue A., Gabrys R., Horvath L., Kokoszka P.. Estimation of a change-point in the mean function of functional data. J. Multivariate Anal., 2009, 100: 2254-2269

[2] Bai J.. Least squares estimation of a shift in linear process. J. Time Ser. Anal., 1994, 15: 453-472

[3] Bai J., Perron P.. Estimating and testing linear models with multiple structural changes. Econometrica, 1998, 66: 47-78

[4] Braun J. V., Braun R. K., Muller H. G.. Multiple changepoint fitting via quasilikelihood, with application to DNA sequence segmentation. Biometrika, 2000, 87(2): 301-314

[5] Chen G., Choi Y. K., Zhou Y.. Nonparametric estimation of structural change points in volatility models for time series. J. Econometrics, 2005, 126: 79-114

[6] Chen G., Choi Y. K., Zhou Y.. Detections of changes in return by a wavelet smoother with conditional heteroscedastic volatility. J. Econometrics, 2008, 143: 227-262

[7] Chen X. R.. Inference in a simple change-point model. Scientia Sinica A, 1988, 6: 654-667

[8] Cheon S., Kim J.. Multiple change-point detection of multivariate mean vectors with the Bayesian approach. Comput. Statist. Data Anal., 2010, 54: 406-415

[9] Chernoff H., Zacks S.. Estimating the current mean of normal distribution which is subjected to change in time. Ann. Statist., 1964, 35: 999-1018

[10] Csörgö M., Horváth L.. Limit Theorems in Change-Points Analysis, 1997, New York: John Wily and Sons

[11] Daniel B. D., Hartigan J. A.. A Bayesian analysis for change point problems. J. Amer. Statist. Assoc., 1993, 88: 309-319

[12] Fotopoulos S., Jandhyala V.. Maximum likelihood estimation of a change-point for exponentially distributed random variables. Statist. Probab. Lett., 2001, 51: 423-429

[13] Grabovsky I., Horváth L., Hušková M.. Limit theorems for kernel-type estimators for the time of change. J. Statist. Plann. Inference, 2000, 89: 26-56

[14] Hinkley D. V.. Inference in two-phase regression. J. Amer. Statist. Assoc., 1971, 66: 736-743

[15] Huskova M., Prakova Z., Steinebach J.. On the detection of changes in autoregressive time series I asymptotics. J. Statist. Plann. Inference, 2007, 137: 1243-1259

[16] Miao B. Q.. Inference in a model with at most one slope-change point. J. Multivariate Anal., 1988, 27: 375-391

[17] Pan J., Chen J.. Application of modified information criterion to multiple change point problems. J. Multivariate Anal., 2006, 97: 2221-2241

[18] Perron P., Qu Z.. Estimating restricted structural change models. J. Econometrics, 2006, 134(2): 373-399

[19] Ramanayake A., Gupta A. K.. Change points with linear trend followed by abrupt change for the exponential distribution. J. Stat. Comput. Simul., 2002, 72(4): 263-278

[20] Rudoy D., Yuen S. G., Howe R. D., Wolfe P. J.. Bayesian change-point analysis for atomic force microscopy and soft material indentation. J. Roy. Statist. Soc. Ser. C, 2010, 59: 1-21

[21] Sertkaya D., Kadilar C.. A new Bayes estimate of the change point in the hazard function. Comput. Statist. Data Anal., 2007, 51: 2993-3001

[22] Tan C. C., Niu H. F., Miao B. Q.. Convergence rate for the change-point estimator in a simple change-point model (in Chinese). Chin. Ann. Math., 2010, 31A(3): 257-264

[23] Tan, C. C., Hui, J. and Miao, B.Q., O _P convergence rate for the jump change-point estimator (in Chinese), J. Systems Sci. Math. Sci., 2012, to appear.

[24] Wu Y.. Simultaneous change point analysis and variable selection in a regression problem. J. Multivariate Anal., 2008, 99: 2154-2171