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2015 Bootstrap consistency for quadratic forms of sample averages with increasing dimension
Demian Pouzo
Electron. J. Statist. 9(2): 3046-3097 (2015). DOI: 10.1214/15-EJS1090

Abstract

This paper establishes consistency of the weighted bootstrap for quadratic forms $\left(n^{-1/2}\sum_{i=1}^{n}Z_{i,n} \right)^{T}\left(n^{-1/2}\sum_{i=1}^{n}Z_{i,n}\right)$ where $(Z_{i,n})_{i=1}^{n}$ are mean zero, independent $\mathbb{R}^{d}$-valued random variables and $d=d(n)$ is allowed to grow with the sample size $n$, slower than $n^{1/4}$. The proof relies on an adaptation of Lindeberg interpolation technique whereby we simplify the original problem to a Gaussian approximation problem. We apply our bootstrap results to model-specification testing problems when the number of moments is allowed to grow with the sample size.

Citation

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Demian Pouzo. "Bootstrap consistency for quadratic forms of sample averages with increasing dimension." Electron. J. Statist. 9 (2) 3046 - 3097, 2015. https://doi.org/10.1214/15-EJS1090

Information

Received: 1 December 2014; Published: 2015
First available in Project Euclid: 19 January 2016

zbMATH: 1384.62157
MathSciNet: MR3450756
Digital Object Identifier: 10.1214/15-EJS1090

Subjects:
Primary: 60F05, 60F17, 62E20, 62F40

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.9 • No. 2 • 2015
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