Change-Point Problems
23 Dec 2011 14:48
Suppose you have a time series which has some (stochastic) property you're interested in, say its expected value or its variance. You think this is usually constant, but that if it does change, it does so abruptly. You would like to know if and when it changes, and perhaps to localize the time when it did. You now have a change-point problem.
See also: Time Series; Non-Stationary Forecasting; Filtering and State Estimation
- Recommended:
- Sylvain Arlot and Alain Celisse, "Segmentation of the mean of heteroscedastic data via cross-validation", Statistics and Computing 21 (2011): 613--632, arxiv:0902.3977 [MATLAB code]
- Emily B. Fox, Erik B. Sudderth, Michael I. Jordan, Alan S. Willsky, "A sticky HDP-HMM with application to speaker diarization", Annals of Applied Statistics 5 (2011): 1020--1056, arxiv:0905.2592
- Daniil Ryabko and Boris Ryabko, "Testing Statistical Hypotheses About Ergodic Processes", arxiv:0804.0510 [Appears to be the same as their "Nonparametric Statistical Inference for Ergodic Processes", IEEE Transactions on Information Theory 56 (2010): 1430--1435
- Wenguang Sun, T. Tony Cai, "Large-scale multiple testing under dependence", Journal of the Royal Statistical Society B 71 (2008): 393--424
- Albert Vexler, "Martingale Type Statistics Applied to Change Point Detection", Communications in Statistics - Theory and Methods 37 (2008): 1207--1224
- To read:
- Boris Brodsky and Boris Darkhovsky, "Sequential change-point detection for mixing random sequences under composite hypotheses", Statistical Inference for Stochastic Processes 11 (2008): 35--54
- S. Camargo, S. M. Duarte Quieros and C. Anteneodo, "Nonparametric segmentation of nonstationary time series", Physical Review E 84 (2011): 046702
- Cheng-Der Fuh
- "SPRT and CUSUM in hidden Markov models", Annals of Statistics 31 (2003): 942--977
- "Asymptotic operating characteristics of an optimal change point detection in hidden Markov models", Annals of Statistics 32 (2004): 2305--2339 = math.ST/0503682
- Samir Ben Hariz, Jonathan J. Wylie, Qiang Zhang, "Optimal rate of convergence for nonparametric change-point estimators for nonstationary sequences", Annals of Statistics 35 (2007): 1802--1826, arxiv:0710.4217
- Heping He and Thomas A. Severini, "Asymptotic properties of maximum likelihood estimators in models with multiple change points", Bernoulli 16 (2010): 759--779, arxiv:1102.5224
- C. T. Jose, B. Ismail, S. Jayasekhar, "Trend, Growth Rate, and Change Point Analysis: A Data Driven Approach", Communications in Statistics: Simulation and Computation 37 (2008): 498--506
- Shiqing Ling, "Testing for change points in time series models and limiting theorems for NED sequences", Annals of Statistics 35 (2007): 1213--1237, arxiv:0708.2369
- George V. Moustakides, "Sequential change detection revisited", arxiv:0804.0741 = Annals of Statistics 36 (2008): 787--807
