Mathematics – Statistics Theory
Scientific paper
2006-06-28
Annals of Statistics 2007, Vol. 35, No. 3, 1324-1350
Mathematics
Statistics Theory
Published at http://dx.doi.org/10.1214/009053607000000190 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053607000000190
Let $\{X_i\}_{i=-\infty}^{\infty}$ 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.
No associations
LandOfFree
Asymptotic expansions for sums of block-variables under weak dependence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Asymptotic expansions for sums of block-variables under weak dependence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic expansions for sums of block-variables under weak dependence will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-598179