Electronic Journal of Statistics

Bootstrap consistency for quadratic forms of sample averages with increasing dimension

Demian Pouzo

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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.

Article information

Electron. J. Statist., Volume 9, Number 2 (2015), 3046-3097.

Received: December 2014
First available in Project Euclid: 19 January 2016

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles 62E20: Asymptotic distribution theory 62F40: Bootstrap, jackknife and other resampling methods

Asymptotic theory bootstrap high dimensional statistics quadratic forms model specification test


Pouzo, Demian. Bootstrap consistency for quadratic forms of sample averages with increasing dimension. Electron. J. Statist. 9 (2015), no. 2, 3046--3097. doi:10.1214/15-EJS1090. https://projecteuclid.org/euclid.ejs/1453212364

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