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Product partition models for change point problems. (English) Zbl 0780.62071
Product partition models assume that observations in different components of a random partition of the data are independent. These models apply with special computational simplicity to change point problems, where the partitions divide the sequence of observations into components within which different regimes hold. It is shown that the observations can determine approximately the true partition when appropriate selection of prior product models is made.
Y.-C. Yao’s method [Stat. Probab. Lett. 6, 181-189 (1988; Zbl 0642.62016)] of selecting change points is compared with the product partition method. More extensive simulation studies have shown that the mean square errors in estimating means at each point are higher for the G. Schwarz [Ann. Statist. 6, 461-464 (1978; Zbl 0379.62005)] selection method than appropriate product partition methods, even though the product partition method overestimates the number of groups.

62M20 Inference from stochastic processes and prediction
62G05 Nonparametric estimation
93E14 Data smoothing in stochastic control theory
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