Symmetric Quantile Averages and Related Estimators
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The average of two complementary order statistics is termed a symmetric quantile average. In addition to having quite good efficiency, robustness and computational properties, exact nonparametric confidence intervals for location can be derived from it. A related type of estimator called a combined quantile average is introduced; it is slightly more difficult to compute than the symmetric quantile average, but can have better efficiency and robustness properties. In fact the recommended form of combined quantile average is comparable for robustness and normal efficiency with the 15% trimmed mean, but in addition it leads, like symmetric quantile averages, to the definition of exact nonparametric confidence intervals.
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异质性高维分位数回归的全局推断
Quantile regression has received considerable attention in high dimensional methodology due to its robustness and ability to accommodate heteroskedasticity. Despite this attention, current inferential methods for high dimensional quantile regression have significant limitations---only testing significance, testing at a single quantile at a time, or assuming homoskedasticity. To generalize the inferences that can be drawn in high dimensional quantile regression, we introduce…
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We first provide inference on the quantile function of the bid distribution in firstprice or descending auctions, and the quantile function of the value distribution in second-price or ascending auctions, with a known number of bidders with symmetric independent private values. Specifically, we provide finite-sample, nonparametric, tuning parameter-free, uniform confidence bands for these quantile functions when observing only the transaction price. We also show how these…
条件影响函数
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Randomized experiments with ordinal outcomes are common across scientific applications, but conventional causal estimands such as the average treatment effect are difficult to interpret because ordinal categories lack meaningful numerical spacing. Two interpretable estimands, the probabilities that the treatment is beneficial and strictly beneficial, depend on the joint distribution of the potential outcomes and are therefore not identifiable from observed data. The sharp…
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In spatial observational studies, treatment assignment and outcomes often exhibit spatial dependence patterns, and treatment effects may vary across space and subpopulations due to both measured and unmeasured spatially structured confounders. Accounting for spatial dependence while estimating heterogeneous treatment effects (HTEs) is a central task in spatial causal inference. Causal Bayesian additive regression tree methods are popular nonparametric methods for modeling…