arXiv 11 Nov 2014 · Mathematics — Statistics Theory · publishedElectronic Journal of Statistics (2014) · 2 citations (OpenAlex)
arXiv:1411.2701 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chernozhukov, V., Chetverikov, D., and Kato, K (2013) Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors | 0.950 | 7 | 4 | 86% |
| 2 | Rollin, A (2013) Stein's method in high dimensions with applications | 0.928 | 5 | 3 | 80% |
| 3 | Donald, S., Imbens, G., and Newey, W (2003) Empirical likelihood estimation and consistent tests with conditional moment restrictions | 0.874 | 5 | 2 | 100% |
| 4 | Van der Vaart, A (2000) Asymptotic Statistics\/ | 0.843 | 3 | 3 | 100% |
| 5 | Peng, H. and Schick, A (2012) Asymptotic normality of quadratic forms with random vectors of increasing dimension | 0.737 | 3 | 2 | 100% |
| 6 | Xu, M., Zhang, D., and Wu, W. B (2014) $L^2$ asymptotics for high-dimensional data | 0.737 | 3 | 2 | 100% |
| 7 | Boucheron, S., Lugosi, G., and Massart, P (2013) Concentration Inequalities\/ | 0.644 | 2 | 2 | 100% |
| 8 | Chernozhukov, V., Chetverikov, D., and Kato, K (2013) Comparison and anti-concentration bounds for maxima of Gaussian random vectors | 0.644 | 2 | 2 | 100% |
| 9 | Chatterjee, S (2006) A generalization of the Lindeberg principle | 0.644 | 2 | 2 | 100% |
| 10 | Chen, X. and Pouzo, D (2015) Sieve Wald and QLR inferences on semi/nonparametric conditional moment models self | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 49 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Bootstrapping $_p$-Statistics in High Dimensions | 0.644 | 2 | 2 |
| 2 | Learning non-smooth models: instrumental variable quantile regressions and related problems | 0.405 | 1 | 1 |
| 3 | An Identification-and Dimensionality-Robust Test for Instrumental Variables Models | 0.405 | 1 | 1 |