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高维 U 统计量中显式依赖阶数的线性化AI 解读

We give an order-explicit large deviation bound for the difference between a high-dimensional $U$-statistic and its Hájek projection. In particular, we show that any $U$-statistic of order $b$ on $n$ observations, with a $d$-dimensional kernel whose coordinates have $ψ_1$-Orlicz norm at most $φ$, has a maximum deviation from its Hájek projection of order $O_p(φb n^{-1}\log^2(dn))$. The proof relies on the development of novel order-explicit moment inequalities for…

利用多个结果变量校正空间相关标准误AI 解读

Empirical research in economics often examines the behavior of agents located in a geographic space. In such cases, statistical inference is complicated by the interdependence of economic outcomes across locations. A common approach to account for this dependence is to cluster standard errors based on a predefined geographic partition. A second strategy is to model dependence in terms of the distance between units. Dependence, however, does not necessarily stop at borders…

随机化推断：理论与应用AI 解读

We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization tests achieve exact control of the Type I error rate in finite samples. Although this unequivocal precision is very appealing, the range of problems that satisfy the randomization hypothesis is somewhat limited. We show that randomization…

样本分割统计量的可复现聚合AI 解读

Statistical inference is often simplified by sample-splitting. This simplification comes at the cost of the introduction of randomness not native to the data. We propose a simple procedure for sequentially aggregating statistics constructed with multiple splits of the same sample. The user specifies a bound and a nominal error rate. If the procedure is implemented twice on the same data, the nominal error rate approximates the chance that the results differ by more than the…

长期处理效应的半参数估计AI 解读

Long-term outcomes of experimental evaluations are necessarily observed after long delays. We develop semiparametric methods for combining the short-term outcomes of experiments with observational measurements of short-term and long-term outcomes, in order to estimate long-term treatment effects. We characterize semiparametric efficiency bounds for various instances of this problem. These calculations facilitate the construction of several estimators. We analyze the…