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摘要翻译：
分位数回归(QR)是分析协变量对结果影响的主要回归方法。这种影响由条件分位数函数及其函数描述。本文发展了非参数QR级数框架，作为一个特例，复盖了许多回归子，用于对整个条件分位数函数及其线性函数进行推理。在这个框架中，我们通过级数项与分位数特定系数的线性组合来逼近整个条件分位数函数，并从数据中估计函数值系数。我们发展了QR级数系数过程的大样本理论，即通过条件关键过程和高斯过程获得了QR级数系数过程的一致强逼近。基于这些强近似或耦合，我们开发了四种重采样方法（枢轴法、梯度自举法、高斯法和加权自举法），可以用于整个QR级数系数函数的推断。利用这些结果，我们得到了条件分位数函数的线性函数的估计和推断方法，如条件分位数函数本身、它的偏导数、平均偏导数和条件平均偏导数。具体来说，我们得到了一致的收敛速度，并展示了如何使用上述四种重采样方法对泛函进行推理。以上所有结果都是针对函数值参数的，在分位数指数和协变量值中都保持一致，并作为副产品覆盖了点态情况。我们通过一个例子证明了这些结果的实际效用，在这个例子中，我们估计了价格弹性函数，并检验了以个体未观察到的汽油消费倾向为指标的个体汽油需求的Slutsky条件。
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英文标题：
《Conditional Quantile Processes based on Series or Many Regressors》
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作者：
Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov and Iv\'an
Fern\'andez-Val
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最新提交年份：
2018
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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：
Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR-series framework, covering many regressors as a special case, for performing inference on the entire conditional quantile function and its linear functionals. In this framework, we approximate the entire conditional quantile function by a linear combination of series terms with quantile-specific coefficients and estimate the function-valued coefficients from the data. We develop large sample theory for the QR-series coefficient process, namely we obtain uniform strong approximations to the QR-series coefficient process by conditionally pivotal and Gaussian processes. Based on these strong approximations, or couplings, we develop four resampling methods (pivotal, gradient bootstrap, Gaussian, and weighted bootstrap) that can be used for inference on the entire QR-series coefficient function. We apply these results to obtain estimation and inference methods for linear functionals of the conditional quantile function, such as the conditional quantile function itself, its partial derivatives, average partial derivatives, and conditional average partial derivatives. Specifically, we obtain uniform rates of convergence and show how to use the four resampling methods mentioned above for inference on the functionals. All of the above results are for function-valued parameters, holding uniformly in both the quantile index and the covariate value, and covering the pointwise case as a by-product. We demonstrate the practical utility of these results with an example, where we estimate the price elasticity function and test the Slutsky condition of the individual demand for gasoline, as indexed by the individual unobserved propensity for gasoline consumption.
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PDF链接：
https://arxiv.org/pdf/1105.6154
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