The geometric convergence rate of the classical change-point estimate

Stergios Fotopoulos ()

Statistics & Probability Letters, 2009, vol. 79, issue 2, 131-137

Abstract: An analytic method for obtaining optimum rates of convergence for the total variation distances is established. The distance engages the distribution of the maximum likelihood estimate of the change-point in a fixed sample size time ordered data and the distribution of the maximum likelihood estimate of the change-point in an infinite time series data. The method is based purely on probabilistic arguments. Various ideas from random walks, supermartingales, ladder heights, and a recursive sequence of embedded random walks are considered. The optimum rate factor involves the probability of the first passage time to the positive axis.

Date: 2009
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