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oct 2000 The multiple change-points problem for the spectral distribution
Marc Lavielle, Carenne Ludeña
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Bernoulli 6(5): 845-869 (oct 2000).

Abstract

We consider the problem of detecting an unknown number of change-points in the spectrum of a second-order stationary random process. To reach this goal, some maximal inequalities for quadratic forms are first given under very weak assumptions. In a parametric framework, and when the number of changes is known, the change-point instants and the parameter vector are estimated using the Whittle pseudo-likelihood of the observations. A penalized minimum contrast estimate is proposed when the number of changes is unknown. The statistical properties of these estimates hold for strongly mixing and also long-range dependent processes. Estimation in a nonparametric framework is also considered, by using the spectral measure function. We conclude with an application to electroencephalogram analysis.

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Marc Lavielle. Carenne Ludeña. "The multiple change-points problem for the spectral distribution." Bernoulli 6 (5) 845 - 869, oct 2000.

Information

Published: oct 2000
First available in Project Euclid: 6 April 2004

zbMATH: 0998.62077
MathSciNet: MR2001I:62098

Keywords: detection of change-points , Long range dependence , maximal inequality , nonparametric spectral estimation , penalized minimum contrast estimate , Quadratic forms , Whittle likelihood

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability

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Vol.6 • No. 5 • oct 2000
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