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Robust Instrumental Variables: Sharp Rates and Inference under Adversarial Contamination

稳健工具变量:对抗污染下的精确收敛率与推断

Because 2SLS is built from sample averages, a small number of observations can have a disproportionate effect on estimates and inference. We introduce W-2SLS, a simple drop-in robustification that replaces these averages by quantile-winsorized means. We analyze W-2SLS under adversarial contamination, which permits both the identities and the reported values of the contaminated observations to depend on the realized clean sample and therefore accommodates targeted or…

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A Necessary and Sufficient Condition for Size Controllability of Heteroskedasticity Robust Test Statistics

异方差稳健检验统计量水平可控性的充要条件

We revisit size controllability results in Pötscher and Preinerstorfer (2025) concerning heteroskedasticity robust test statistics in regression models. For the special, but important, case of testing a single restriction (e.g., a zero restriction on a single coefficient), we povide a necessary and sufficient condition for size controllability, whereas the condition in Pötscher and Preinerstorfer (2025) is, in general, only sufficient (even in the case of testing a single…

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Regularizing Fairness in Optimal Policy Learning with Distributional Targets

具有分布目标的最优政策学习中的公平性正则化

A decision maker typically (i) incorporates training data to learn about the relative effectiveness of treatments, and (ii) chooses an implementation mechanism that implies an ``optimal'' predicted outcome distribution according to some target functional. Nevertheless, a fairness-aware decision maker may not be satisfied achieving said optimality at the cost of being ``unfair" against a subgroup of the population, in the sense that the outcome distribution in that subgroup…

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Enhanced power enhancements for testing many moment equalities: Beyond the $2$- and $\infty$-norm

多重矩等式检验的功效增强:超越二范数与无穷范数

Contemporary testing problems in statistics are increasingly complex, i.e., high-dimensional. Tests based on the $2$- and $\infty$-norm have received considerable attention in such settings, as they are powerful against dense and sparse alternatives, respectively. The power enhancement principle of Fan et al. (2015) combines these two norms to construct improved tests that are powerful against both types of alternatives. In the context of testing whether a candidate…

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A remark on moment-dependent phase transitions in high-dimensional Gaussian approximations

关于高维高斯近似中依赖矩条件的相变

In this article, we study the critical growth rates of dimension below which Gaussian critical values can be used for hypothesis testing but beyond which they cannot. We are particularly interested in how these growth rates depend on the number of moments that the observations possess.

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A Modern Gauss-Markov Theorem? Really?

现代 Gauss–Markov 定理?果真如此?

We show that the theorems in Hansen (2021a) (the version accepted by Econometrica), except for one, are not new as they coincide with classical theorems like the good old Gauss-Markov or Aitken Theorem, respectively; the exceptional theorem is incorrect. Hansen (2021b) corrects this theorem. As a result, all theorems in the latter version coincide with the above mentioned classical theorems. Furthermore, we also show that the theorems in Hansen (2022) (the version published…

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Valid Heteroskedasticity Robust Testing

有效的异方差稳健检验

Tests based on heteroskedasticity robust standard errors are an important technique in econometric practice. Choosing the right critical value, however, is not simple at all: conventional critical values based on asymptotics often lead to severe size distortions; and so do existing adjustments including the bootstrap. To avoid these issues, we suggest to use smallest size-controlling critical values, the generic existence of which we prove in this article for the commonly…

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Superconsistency of Tests in High Dimensions

高维检验的超一致性

To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests is available, each test has its strengths but also its blind spots. In a Gaussian sequence model, we study whether it is possible to obtain a test with substantially better consistency properties than the likelihood ratio (i.e., Euclidean…

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