Estimating the number of change points in a sequence of independent normal random variables

Lee, Chung-Bow

doi:10.1016/0167-7152(94)00227-y

Cited by 27 publications

(16 citation statements)

References 5 publications

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“…Here j 0 0 and j k1 n; the values d(n) and d Ã 0 (n) will be given in assumption (ii) and (iii) respectively later. The criterion in (1.2) is similar to those given by Schwarz (1978), Yao (1988) and Lee (1995). We ®nd that, under mild assumptions, the estimator k to maximize the criterion in (1.2) will be consistent for the true number k 0 of change points with probability approaching 1 as n 3 I and the difference between the estimated change location j(k 0 ) ( j 1 , X X X, j k 0 ) and the true change location j 0 (k 0 ) ( j 0 1 , X X X, j 0 k0 ) will be bounded by order O p (d Ã 0 (n))X Here ( È, j(k 0 )) is the maximum likelihood estimator for f (X ; È, j(k 0 ), k 0 ) under the constraint j j i À j iÀ1 j > d Ã 0 (n), i 1, 2, X X X, k 0 1X Schwarz (1978) considered the problem of model selection based on decision theory for exponential families with different dimensional parameters and obtained an asymptotically optimal solution to choose the model for which…”

Section: Introductionsupporting

confidence: 63%

“…where ó 2 k is the maximum likelihood estimator of ó 2 given ®xed k. He found that, under mild assumptions, the estimator k Ã will converge to the true number of change points with probability approaching 1 as n 3 I. Lee (1995) also considered the problem given by Yao (1988) but with a different penalty term d(n) and obtained the consistency for the estimator to maximize…”

Section: Introductionmentioning

confidence: 99%

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Estimating the Number of Change Points in Exponential Families Distributions

Lee

1997

Scandinavian J Statistics

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A simple method is proposed to detect the number of change points in a sequence of independent exponential family random variables. An estimator to maximize some criterion, say SC(k), which is to maximize the log-likelihood function with some penalty term, is used in detection. Under some mild assumptions, the consistency of the estimator for the true number of change points and the boundedness between the estimated change locations and the true change location are obtained. Some simulated results are given, and the Nile problem is investigated by this method.

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Section: Introductionsupporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Estimating the Number of Change Points in Exponential Families Distributions

Lee

1997

Scandinavian J Statistics

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“…They then either minimise a penalised version of this cost (e.g. Yao 1988;Lee 1995), which we call the penalised minimisation problem; or minimise the cost under a constraint on the number of changepoints (e.g. Yao and Au 1989;Braun and Müller 1998), which we call the constrained minimisation problem.…”

Section: Introductionmentioning

confidence: 99%

On optimal multiple changepoint algorithms for large data

et al. 2016

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Many common approaches to detecting changepoints, for example based on statistical criteria such as penalised likelihood or minimum description length, can be formulated in terms of minimising a cost over segmentations. We focus on a class of dynamic programming algorithms that can solve the resulting minimisation problem exactly, and thus find the optimal segmentation under the given statistical criteria. The standard implementation of these dynamic programming methods have a computational cost that scales at least quadratically in the length of the time-series. Recently pruning ideas have been suggested that can speed up the dynamic programming algorithms, whilst still being guaranteed to be optimal, in that they find the true minimum of the cost function. Here we extend these pruning methods, and introduce two new algorithms for segmenting data: FPOP and SNIP. Empirical results show that FPOP is substantially faster than existing dynamic programming methods, and unlike the existing methods its computational efficiency is robust to the number of changepoints in the data. We evaluate the method for detecting copy number variations and observe that FPOP has a computational cost that is even competitive with that of binary segmentation, but can give much more accurate segmentations.

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“…Different statistical approaches are continuously derived in the area over the last few decades. Related work can be seen in Hawkins (1976), Worsley (1986), Yao (1988), Lee (1995), Chen and Gupta (2003) and the references therein. On the other hand, it is more plausible that there exist multiple change points in large date sets.…”

Section: Introductionmentioning

confidence: 97%