A0320
Title: Yurinskii's coupling for martingales
Authors: Ricardo Masini - UC Davis (United States) [presenting]
Abstract: Yurinskii's coupling is a popular theoretical tool for non-asymptotic distributional analysis in mathematical statistics and applied probability, offering a strong Gaussian approximation with an explicit error bound under easily verified conditions. Originally started 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. As the main result is presented, a Yurinskii coupling for approximate martingales in $\ell^p$-norm, under substantially weaker conditions than those previously imposed. The formulation further allows for the coupling variable to follow a more general Gaussian mixture distribution, and a novel third-order coupling method is provided that gives tighter approximations in certain settings. The main result specializes in mixingales, martingales, and independent data, and uniform Gaussian mixture strong approximations are derived for martingale empirical processes. Applications to non-parametric partitioning-based and local polynomial regression procedures are provided.
