Matias D. Cattaneo, Ricardo P. Masini, William G. Underwood
arXiv 1 Oct 2022 · Mathematics — Statistics Theory · publishedThe Annals of Statistics (2025) · 3 citations (OpenAlex)
arXiv:2210.00362 · PDF · DOI · OpenAlex · Extracted main text
Yurinskii's coupling is a popular theoretical tool for non-asymptotic distributional analysis in mathematical statistics and applied probability, offering a Gaussian strong approximation with an explicit error bound under easily verifiable conditions. Originally stated in $\ell_2$-norm for sums of independent random vectors, it has recently been extended both to the $\ell_p$-norm, for $1 \leq p \leq \infty$, and to vector-valued martingales in $\ell_2$-norm, under some strong conditions. We present as our main result a Yurinskii coupling for approximate martingales in $\ell_p$-norm, under substantially weaker conditions than those previously imposed. Our formulation further allows for the coupling variable to follow a more general Gaussian mixture distribution, and we provide a novel third-order coupling method which gives tighter approximations in certain settings. We specialize our main result to mixingales, martingales, and independent data, and derive uniform Gaussian mixture strong approximations for martingale empirical processes. Applications to nonparametric partitioning-based and local polynomial regression procedures are provided, alongside central limit theorems for high-dimensional martingale vectors.
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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 | Li, J. and Liao, Z (2020) Uniform nonparametric inference for time series | 1.000 | 20 | 4 | 100% |
| 2 | Belloni, A. and Oliveira, R. I (2018) A high dimensional central limit theorem for martingales, with applications to context tree models | 0.956 | 8 | 3 | 88% |
| 3 | Chernozhukov, V., Chetverikov, D., and Kato, K (2014) Gaussian approximation of suprema of empirical processes | 0.928 | 5 | 4 | 80% |
| 4 | Pollard, D (2002) A User's Guide to Measure Theoretic Probability | 0.928 | 5 | 3 | 80% |
| cattaneo2025yurinskiisupplement | unmatched citation key cattaneo2025yurinskiisupplement | 0.894 | 14 | 5 | 71% |
| 6 | Berthet, P. and Mason, D. M (2006) Revisiting two strong approximation results of Dudley and Philipp | 0.874 | 6 | 2 | 100% |
| 7 | Belloni, A., Chernozhukov, V., Chetverikov, D., and Fernández-Val, I (2019) Conditional quantile processes based on series or many regressors | 0.843 | 4 | 3 | 75% |
| 8 | van der Vaart, A. W. and Wellner, J. A (1996) Weak Convergence and Empirical Processes | 0.843 | 10 | 3 | 60% |
| 9 | Komlós, J., Major, P., and Tusnády, G (1975) An approximation of partial sums of independent RVs, and the sample DF. I | 0.843 | 3 | 3 | 100% |
| 10 | Cattaneo, M. D., Farrell, M. H., and Feng, Y (2020) Large sample properties of partitioning-based series estimators self | 0.822 | 9 | 3 | 56% |
Showing the top 10 of 63 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A maximal inequality for local empirical processes under weak dependence | 0.511 | 2 | 1 |
| 2 | Adjustments with Many Regressors under Covariate-Adaptive Randomizations | 0.405 | 1 | 1 |
| 3 | Uniform Estimation and Inference for Nonparametric Partitioning-Based M-Estimators | 0.000 | 2 | 2 |