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

Bootstrap Consistency for Quadratic Forms of Sample Averages with Increasing Dimension