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Article Dans Une Revue Mathematical Methods of Statistics Année : 2011

A Renewal Approach to Markovian U-statistics

Résumé

In this paper we describe a novel approach to the study of U-statistics in the markovian setup, based on the (pseudo-) regenerative properties of Harris Markov chains. Exploiting the fact that any sample path X1, . . . , Xn of a general Harris chain X may be divided into asymptotically i.i.d. data blocks B1, . . . , BN of ran- dom length corresponding to successive (pseudo-) regeneration times, we introduce the notion of regenerative U-statistic ΩN =
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Dates et versions

hal-00442278 , version 1 (18-12-2009)
hal-00442278 , version 2 (09-07-2010)

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Patrice Bertail, Stéphan Clémençon. A Renewal Approach to Markovian U-statistics. Mathematical Methods of Statistics, 2011, 20 (2), pp.79-105. ⟨10.3103/S1066530711020013⟩. ⟨hal-00442278v2⟩
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