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鞅的Yurinskii耦合AI 解读

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…

通过 Copula 建立极值统计量的锐反集中不等式AI 解读

We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal law of the samples or on the copula describing their joint distribution. We show that, in general, strictly sublinear dependence of the concentration function on the dimension $d$ is not possible. We then introduce a new class of copulas,…

反事实分析是否充分利用信息？因子模型与特异成分修正的作用AI 解读

Optimal pricing, i.e., determining the price level that maximizes profit or revenue of a given product, is a vital task for the retail industry. To select such a quantity, one needs first to estimate the price elasticity from the product demand. Regression methods usually fail to recover such elasticities due to confounding effects and price endogeneity. Therefore, randomized experiments are typically required. However, elasticities can be highly heterogeneous depending on…