Sequential change-point detection for mixing random sequences under composite hypotheses |
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Authors: | Boris Brodsky Boris Darkhovsky |
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Institution: | (1) Central Institute for Mathematics and Economics RAS, 47, Nakhimovsky prospekt, 117418 Moscow, Russia;(2) Institute for Systems Analysis RAS, 9, prospekt 60-letya, Oktyabria, 117312 Moscow, Russia |
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Abstract: | The problem of sequential detection of a change-point in the density function of one-dimensional distribution of observations
from a mixing random sequence is considered when both before and after a change-point this density function belongs to a certain
family of distributions, i.e. in the situation of composite hypotheses. A new quality criterion for change-point detection
is proposed. The asymptotic a priori lower bound for this criterion is proved for wide class of methods of change-point detection.
An asymptotically optimal method of change-point detection is proposed for which this lower bound is attained asymptotically.
In particular, for the case of a simple hypothesis before a change-point, this method coincides with the generalized cumulative
sums (CUSUM) method.
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Keywords: | Change-point problem Composite hypotheses |
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