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A Fast Two-Stage Algorithm by Window Method for Estimating the Location of Change-Points
|關鍵字:||Change-points;改變點;Exponential family;Dynamic programming;Segmental K-means;Bayesian information criteria;指數家族;動態程序;K均值分割;貝氏訊息準則||出版社:||應用數學系所||引用:|| Akaike, H. (1973). Information theory and an extension of the maximum likeli-hood principle. 2nd International Symposium of Information Theory. 267-281.  Bellman, R. E. (1957). Dynamic Programming, Princeton University, Princeton.  Bhattacharyya, G. K. and Johnson, R. A. (1968). Non-parametric tests for shift at an unknown time point. Annals of Mathematical Statistics 39, 1731-1743.  Boukai, B. (1994). Graphically based interval estimation for the change-point. Computational Statistics & Data Analysis 17, 77-86.  Braun, J. V., Braun, R. K. and Muller, H. G. (2000). Multiple changepoint fitting via quasilikelihood, with application to DNA sequence segmentation. Biometrika 87, 301-314.  Braun, J. V. and Muller, H. G. (1998). Statistical Methods for DNA Sequence Segmentation. Statistical Science 13, 42-162  Carlstein, E. (1988). 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Statistics & Probability Letters 77, 374-382.||摘要:||
A fast two-stage (TS) algorithm is proposed to estimate the location of change-points in a sequence of independent exponential family random variables. The idea is simple and interesting. In the first stage, we apply the window method by using the log-likelihood ratio measure to find a subset of candidate change-points; and use the dynamic programming (DP) algorithm on the chosen subset to obtain good initial change-points which will be proximate to the locations of the true change-points. In the second stage, the segmental K-means (SKM) algorithm is applied on the initial change-points obtained in the first stage. The real examples obtain Nile data, Dow-Jones industrial data, aircraft arrival data and Well-log data and simulated data sets are investigated. The results show that our algorithm works very well in application. In DP algorithm, the location of each data point is a candidate change-point. Using the window method, we find that the subset of candidate change-points can remove about 74.9% (on average) of change-points from DP algorithm to TS algorithm in real examples. In the comparison of CPU times, the TS algorithm is 24.13 times faster than the DP algorithm. It substantially reduces the heavy computation load for a long sequence of data. For simulated data sets, the performance of DP and TS algorithm are almost same in the estimation errors of change-points, but the subset of candidate change-points can remove 75.2 (on average) of change-points. Thus, the speed of TS algorithm can be up to 24.75 and 21.12 times than that of DP algorithm with unknown state and known state, respectively.
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