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异方差稳健检验统计量尺寸可控的充要条件AI 解读

We revisit size controllability results in Pötscher and Preinerstorfer (2025, Econometric Theory 41, 249–301) 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 provide a necessary and sufficient condition for size controllability, whereas the condition in Pötscher and Preinerstorfer (2025, Econometric Theory 41, 249–301) is, in…

多重矩等式检验的功效增强：超越二范数与无穷范数AI 解读

Tests based on the 2- and ∞-norm have received considerable attention in high-dimensional testing problems, 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 parameter satisfies a large number of moment equalities, we construct tests that harness…

分布目标下最优政策学习的公平性正则化AI 解读

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…

有效的异方差稳健检验AI 解读

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…

含协变量的分布泛函序贯处理分配AI 解读

We consider a sequential treatment problem with covariates. Given a realization of the covariate vector, instead of targeting the treatment with highest conditional expectation, the decision-maker targets the treatment which maximizes a general functional of the conditional potential outcome distribution, e.g., a conditional quantile, trimmed mean, or a socioeconomic functional such as an inequality, welfare, or poverty measure. We develop expected regret lower bounds for…

高维检验的超一致性AI 解读

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 (LR; i.e.,…

评《现代高斯—马尔可夫定理》AI 解读

We show that Theorem 4 in Hansen (2022) applies to exactly the same class of estimators as does the classical Aitken theorem. We furthermore point out that Theorems 5–7 in Hansen (2022) contain extra assumptions not present in the classical Gauss–Markov or Aitken theorem, and thus the former theorems do not contain the latter ones as special cases.

如何避免相关性检验中的零功效陷阱AI 解读

In testing for correlation of the errors in regression models, the power of tests can be very low for strongly correlated errors. This counterintuitive phenomenon has become known as the “zero-power trap.” Despite a considerable amount of literature devoted to this problem, mainly focusing on its detection, a convincing solution has not yet been found. In this article, we first discuss theoretical results concerning the occurrence of the zero-power trap phenomenon. Then, we…

基于自助法的异方差稳健检验有多可靠？AI 解读

We develop theoretical finite-sample results concerning the size of wild bootstrap-based heteroskedasticity robust tests in linear regression models. In particular, these results provide an efficient diagnostic check, which can be used to weed out tests that are unreliable for a given testing problem in the sense that they overreject substantially. This allows us to assess the reliability of a large variety of wild bootstrap-based tests in an extensive numerical study.

以分布目标为导向的治疗推荐AI 解读

We study the problem of a decision maker who must provide the best possible treatment recommendation based on an experiment. The desirability of the outcome distribution resulting from the policy recommendation is measured through a functional capturing the distributional characteristic that the decision maker is interested in optimizing. This could be, e.g., its inherent inequality, welfare, level of poverty or its distance to a desired outcome distribution. If the…

Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown which treatment is best, but the sequential nature of the problem permits learning about the effectiveness of the treatments. While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other…

模型选择后具有一致有效性的置信区间AI 解读

We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (Ann. Statist. 41 (2013) 802–837). In particular, the candidate models used can be misspecified, the target of inference is model-specific, and coverage is guaranteed for any data-driven model selection procedure. After developing a general theory, we apply our methods to practically…

高维检验问题中的功效AI 解读

Fan, Liao, and Yao (2015) recently introduced a remarkable method for increasing the asymptotic power of tests in high‐dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, has uniformly non‐inferior asymptotic power, and is consistent against a strictly broader range of alternatives than the initially given test. We study under which conditions this method can be applied…

自相关稳健检验的尺寸控制AI 解读

Autocorrelation robust tests are notorious for suffering from size distortions and power problems. We investigate under which conditions the size of autocorrelation robust tests can be controlled by an appropriate choice of critical value.

协方差矩阵假设的不变检验功效AI 解读

The behavior of the power function of autocorrelation tests such as the Durbin–Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation becomes strong, Krämer (1985, Journal of Econometrics 28, 363–370.) (for the Durbin–Watson test) and Krämer (2005, Journal of Statistical Planning and Inference , 128, 489–496) (for the Cliff-Ord test) have shown that power can be very low,…

异方差与自相关稳健检验的检验水平和功效AI 解读

Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well…