On a multi-channel change-point problem |
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Authors: | A. Korostelev O. Lepski |
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Affiliation: | (1) Wayne State University, Detroit, USA;(2) Université de Provence, Marseille, France |
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Abstract: | A continuous change-point problem is studied in which N independent diffusion processes X j are observed. Each process X j is associated with a “channel”, each has an unknown piecewise constant drift and the unit diffusion coefficient. All the channels are connected only by a common change-point of drift. As the result, a change-point problem is defined in which the unknown and unidentifiable drift forms a 2N-dimensional nuisance parameter. The asymptotics of the minimax rate in estimating the change-point is studied as N → ∞. This rate is compared with the case of the known drift. This problem is a special case of an open change-point detection problem in the high-dimensional diffusion with nonparametric drift. |
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Keywords: | change-point nuisance parameter minimax rate of convergence |
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