## Electronic Journal of Statistics

### Bootstrap consistency for quadratic forms of sample averages with increasing dimension

Demian Pouzo

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 19 January 2016

https://projecteuclid.org/euclid.ejs/1453212364

Digital Object Identifier
doi:10.1214/15-EJS1090

Mathematical Reviews number (MathSciNet)
MR3450756

Zentralblatt MATH identifier
1384.62157

#### Citation

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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