Asymptotic expansions for sums of block-variables under weak dependence

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dc.creatorLahiri, S. N.
dc.date2006-06-28
dc.date2007-08-17
dc.date.accessioned2026-07-07T08:24:49Z
dc.date.available2026-07-07T08:24:49Z
dc.descriptionLet $\{X_i\}_{i=-\infty}^{\infty}$ be a sequence of random vectors and $Y_{in}=f_{in}(\mathcal{X}_{i,\ell})$ be zero mean block-variables where $\mathcal{X}_{i,\ell}=(X_i,...,X_{i+\ell-1}),i\geq 1$, are overlapping blocks of length $\ell$ and where $f_{in}$ are Borel measurable functions. This paper establishes valid joint asymptotic expansions of general orders for the joint distribution of the sums $\sum_{i=1}^nX_i$ and $\sum_{i=1}^nY_{in}$ under weak dependence conditions on the sequence $\{X_i\}_{i=-\infty}^{\infty}$ when the block length $\ell$ grows to infinity. In contrast to the classical Edgeworth expansion results where the terms in the expansions are given by powers of $n^{-1/2}$, the expansions derived here are mixtures of two series, one in powers of $n^{-1/2}$ and the other in powers of $[\frac{n}{\ell}]^{-1/2}$. Applications of the main results to (i) expansions for Studentized statistics of time series data and (ii) second order correctness of the blocks of blocks bootstrap method are given.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053607000000190 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0606739
dc.identifierhttp://arxiv.org/abs/math/0606739
dc.identifierAnnals of Statistics 2007, Vol. 35, No. 3, 1324-1350
dc.identifierdoi:10.1214/009053607000000190
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136470
dc.subjectStatistics Theory
dc.subjectProbability
dc.subject60F05 (Primary); 62E20, 62M10 (Secondary)
dc.titleAsymptotic expansions for sums of block-variables under weak dependence
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