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一阶 Edgeworth 展开误差的显式非渐近界AI 解读

In this article, we obtain explicit bounds on the uniform distance between the cumulative distribution function of a standardized sum $S_n$ of $n$ independent centered random variables with moments of order four and its first-order Edgeworth expansion. Those bounds are valid for any sample size with $n^{-1/2}$ rate under moment conditions only and $n^{-1}$ rate under additional regularity constraints on the tail behavior of the characteristic function of $S_n$. In both…

兼得有限样本有效与一致渐近精确：期望和线性回归的置信区间AI 解读

We contribute to bridging the gap between large- and finite-sample inference by studying confidence sets (CSs) that are both non-asymptotically valid and asymptotically exact uniformly (NAVAE) over semi-parametric statistical models. NAVAE CSs are not easily obtained; for instance, we show they do not exist over the set of Bernoulli distributions. We first derive a generic sufficient condition: NAVAE CSs are available as soon as uniform asymptotically exact CSs are. Second,…