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• W2012077155 abstract "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 X 1, ..., X n of a general Harris chain X may be divided into asymptotically i.i.d. data blocks $mathcal{B}_1 , ldots mathcal{B}_N$ of random length corresponding to successive (pseudo-) regeneration times, we introduce the notion of regenerative U-statistic Ω N = Σ k≠l ω h $left( {mathcal{B}_k ,mathcal{B}_l } right)$ /(N(N − 1)) related to a U-statistic U n = Σ i≠j h(X i , X j )/(n(n − 1)). We show that, under mild conditions, these two statistics are asymptotically equivalent up to the order O ℙ(n−1). This result serves as a basis for establishing limit theorems related to statistics of the same form as U n . Beyond its use as a technical tool for proving results of a theoretical nature, the regenerative method is also employed here in a constructive fashion for estimating the limiting variance or the sampling distribution of certain U-statistics through resampling. The proof of the asymptotic validity of this statistical methodology is provided, together with an illustrative simulation result." @default.
• W2012077155 created "2016-06-24" @default.
• W2012077155 creator A5086542918 @default.
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• W2012077155 date "2011-06-01" @default.
• W2012077155 modified "2023-10-18" @default.
• W2012077155 title "A renewal approach to Markovian U-statistics" @default.
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• W2012077155 doi "https://doi.org/10.3103/s1066530711020013" @default.
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