摘要翻译：
本文提出了一种解决条件分位数函数和结构分位数函数估计缺乏单调性的方法，也称为分位数交叉问题。该方法是将原始估计的非单调曲线排序或单调重排为单调重排曲线。我们证明了在有限样本中重排曲线比原曲线更接近真分位数曲线，建立了重排相关算子的泛函delta方法，并导出了整个重排曲线及其泛函的泛函极限理论。我们还证明了bootstrap估计整个重排曲线及其函数的极限律的有效性。本文的极限结果具有通用性，它适用于单调计量经济函数的每一个估计量，只要估计量满足泛函中心极限定理，且函数满足光滑性条件。因此，我们的结果适用于其他具有单调性限制的计量经济函数的估计，如需求、生产、分配和结构分配函数。我们用越南退伍军人身份和收入数据对结构分位数函数的估计应用来说明结果。
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英文标题：
《Quantile and Probability Curves Without Crossing》
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作者：
Victor Chernozhukov (MIT), Ivan Fernandez-Val (Boston University),
  Alfred Galichon (Ecole Polytechnique)
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最新提交年份：
2014
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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：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：
  This paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions, also known as the quantile crossing problem. The method consists in sorting or monotone rearranging the original estimated non-monotone curve into a monotone rearranged curve. We show that the rearranged curve is closer to the true quantile curve in finite samples than the original curve, establish a functional delta method for rearrangement-related operators, and derive functional limit theory for the entire rearranged curve and its functionals. We also establish validity of the bootstrap for estimating the limit law of the the entire rearranged curve and its functionals. Our limit results are generic in that they apply to every estimator of a monotone econometric function, provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions. Consequently, our results apply to estimation of other econometric functions with monotonicity restrictions, such as demand, production, distribution, and structural distribution functions. We illustrate the results with an application to estimation of structural quantile functions using data on Vietnam veteran status and earnings.
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PDF链接：
https://arxiv.org/pdf/704.3649