摘要翻译：
我们研究了条件分位数估计的小样本性质，如经典分位数和IV分位数回归。首先，我们提出了一个高阶分析框架，用于在小样本中比较竞争估计量，并评估常见推理过程的准确性。我们的框架是基于一种新的不连续样本矩的近似，用一个h\\\\“旧连续过程，误差可以忽略不计。对于任何相合估计量，这种近似导致具有几乎最优速率的渐近线性展开。其次，我们研究精确分位数估计的高阶偏置，直到$O\\left(\\frac{1}{n}\\right)$。利用一种新的非光滑演算技术，我们发现了以前未知的、不能一致估计的、依赖于所采用的估计算法的不可忽略的偏差分量。为了避免这个问题，我们提出了一个“对称”偏差校正，这是一个可行的实现。我们的模拟证实了偏差校正的经验重要性。
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英文标题：
《Conditional quantile estimators: A small sample theory》
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作者：
Grigory Franguridi, Bulat Gafarov, Kaspar Wuthrich
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最新提交年份：
2021
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分类信息：

一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We study the small sample properties of conditional quantile estimators such as classical and IV quantile regression. First, we propose a higher-order analytical framework for comparing competing estimators in small samples and assessing the accuracy of common inference procedures. Our framework is based on a novel approximation of the discontinuous sample moments by a H\\\"older-continuous process with a negligible error. For any consistent estimator, this approximation leads to asymptotic linear expansions with nearly optimal rates. Second, we study the higher-order bias of exact quantile estimators up to $O\\left(\\frac{1}{n}\\right)$. Using a novel non-smooth calculus technique, we uncover previously unknown non-negligible bias components that cannot be consistently estimated and depend on the employed estimation algorithm. To circumvent this problem, we propose a \"symmetric\" bias correction, which admits a feasible implementation. Our simulations confirm the empirical importance of bias correction.
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