摘要翻译：
我们考虑一个随机变量的分布是由该变量的噪声测量的经验分布估计的情形。这是常见的做法，例如，教师增值模型和面板数据的其他固定效应模型。我们使用一种渐近嵌入，其中噪声随样本量的增大而减小，以计算由于噪声的存在而引起的经验分布中的前导偏置。经验分位数函数中的前导偏置是等价的。这些计算在文献中是新的，其中只导出了光滑函数的结果，如均值和方差。给出偏差的闭式表达式，可以构造分布函数和分位数函数的偏差校正估计。我们提供了分析和折刀校正，重新进入极限分布，并在大样本中产生正确覆盖的置信区间。这些校正是非参数的，易于实现。我们的方法可以联系到选择偏差和收缩估计的校正，并将与反卷积进行对比。仿真结果证实了修正后的估计器的采样性能有了很大的改善。
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英文标题：
《Inference on a Distribution from Noisy Draws》
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作者：
Koen Jochmans, Martin Weidner
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最新提交年份：
2019
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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：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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英文摘要：
  We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other fixed-effect models for panel data. We use an asymptotic embedding where the noise shrinks with the sample size to calculate the leading bias in the empirical distribution arising from the presence of noise. The leading bias in the empirical quantile function is equally obtained. These calculations are new in the literature, where only results on smooth functionals such as the mean and variance have been derived. Given a closed-form expression for the bias, bias-corrected estimator of the distribution function and quantile function can be constructed. We provide both analytical and jackknife corrections that recenter the limit distribution and yield confidence intervals with correct coverage in large samples. These corrections are non-parametric and easy to implement. Our approach can be connected to corrections for selection bias and shrinkage estimation and is to be contrasted with deconvolution. Simulation results confirm the much-improved sampling behavior of the corrected estimators.
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PDF链接：
https://arxiv.org/pdf/1803.04991