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鞅的 Yurinskii 耦合AI 解读

Yurinskii’s coupling is a popular theoretical tool for nonasymptotic 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 ℓ2-norm for sums of independent random vectors, it has recently been extended both to the ℓp-norm, for 1≤p≤∞, and to vector-valued martingales in ℓ2-norm, under some strong conditions. We present as our main…

双边关系数据核密度估计的一致推断AI 解读

Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of uniformly estimating a dyadic Lebesgue density function, focusing on nonparametric kernel-based estimators taking the form of dyadic empirical processes. Our main contributions include the minimax-optimal uniform convergence rate of the dyadic…