ESTIMATION OF DISTRIBUTIONS, MOMENTS AND QUANTILES IN DECONVOLUTION PROBLEMS
ESTIMATION OF DISTRIBUTIONS, MOMENTS AND QUANTILES IN DECONVOLUTION PROBLEMS
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DOI：
10.1214/07-aos534
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发表时间：
2008-10-01
影响因子：
4.5
通讯作者：
Lahiri, Soumendra N.
中科院分区：
文献类型：
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作者：
Hall, Peter;Lahiri, Soumendra N.
当在存在测量误差的情况下使用自助法时，我们必须首先估计目标分布函数;我们不能直接重新采样，因为我们没有来自目标的样本。这些和其他考虑因素促使分布估计的发展，以及相关的数量，如矩和分位数，在变量误差的设置。我们表明，这样的估计有好奇和意想不到的属性。例如，如果感兴趣的变量W的分布和观测误差的分布都以零为中心，那么W的分布函数的估计量在原点处的收敛速度可能比远离原点的收敛速度慢。这是问题的内在特征，而不是特定估计量的怪癖：该属性对最优估计量成立。
When using the bootstrap in the presence of measurement error, we must first estimate the target distribution function; we cannot directly resample since we don not have a sample from the target. These and other considerations motivate the development of estimators of distributions, and of related quantities such as moments and quantiles, in errors-in-variables settings. We show that such estimators have curious and unexpected properties. For example, if the distributions of the variable of interest, W, say, and of the observation error are both centered at zero, then the rate of convergence of an estimator of the distribution function of W can be slower at the origin than away from the origin. This is an intrinsic characteristic of the problem, not a quirk of particular estimators: the property holds true for optimal estimators.