The Maximum Likelihood Method for Testing Changes in the Parameters of Normal Observations
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In this paper, the authors compute the asymptotic distribution of the maximum likelihood ratio test when they want to check whether the parameters of normal observations have changed at an unknown point and prove that the limit distribution is based on the largest deviation between a $d$-dimensional Ornstein-Uhlenbeck process and the origin.Abstract:
We compute the asymptotic distribution of the maximum likelihood ratio test when we want to check whether the parameters of normal observations have changed at an unknown point. The proof is based on the limit distribution of the largest deviation between a $d$-dimensional Ornstein-Uhlenbeck process and the origin.read more
Citations
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Optimal Detection of Changepoints With a Linear Computational Cost
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Structural breaks in time series
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Change-point estimation in ARCH models
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TL;DR: In this paper, the cross-covariance function for ARCH models is studied and bounds for the crosscovarisance function are derived and explicit formulae are obtained in special cases.
Journal ArticleDOI
Optimal detection of changepoints with a linear computational cost
TL;DR: In this article, the authors consider the problem of detecting multiple changepoints in large data sets and propose a new method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost which, under mild conditions, is linear in the number of observations.
References
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Diffusion Processes and their Sample Paths.
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On Tests for Detecting Change in Mean
Ashish Sen,Muni S. Srivastava +1 more
TL;DR: In this article, the means of each variable in a sequence of independent random variables can be taken to be the same, against alternatives that a shift might have occurred after some point $r$.
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