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On the rate of almost sure convergence of Dümbgen's change-point estimators

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  • Ferger, Dietmar

Abstract

Consider a triangular array of rowwise independent random elements with values in a measurable space. Suppose there exist [theta]n [set membership, variant]Tn={in-1: 1 [less-than-or-equals, slant]i[less-than-or-equals, slant]n-1} such that X1n,...,Xn,n[theta]n have distribution Pn and Xn,n[theta]n+1,..., Xnn have distribution Qn[not equal to]Pn, where Pn, Qn and [theta]n are unknown. We investigate a large class of change-point estimators n due to Dümbgen. Dümbgen proved that n - [theta]n = Op([gamma]2nn-1), where the sequence ([gamma]n) measures the 'distance' between Pn and Qn. We show that with probability one.

Suggested Citation

  • Ferger, Dietmar, 1994. "On the rate of almost sure convergence of Dümbgen's change-point estimators," Statistics & Probability Letters, Elsevier, vol. 19(1), pages 27-31, January.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:1:p:27-31
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    Cited by:

    1. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.

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