标题： 关于解卷积核密度估计器渐近性的几点思考 显示英文标题

标题： Some thoughts on the asymptotics of the deconvolution kernel density estimator

摘要： 通过模拟研究，我们将超光滑去卷积问题中去卷积核密度估计量的有限样本性能与两个渐近正态性定理所预测的渐近行为进行了比较。 我们的结果显示，在较低噪声水平和适度样本量的情况下，渐近理论与估计器的实际有限样本表现之间的匹配并不令人满意。 另一方面，我们证明了对于较高噪声水平，两种方法产生的结果相当接近。 这些观察结果反过来也为在假设误差项方差 $\sigma^2\to 0$ 随样本量 $n\to\infty.$增大 的情况下研究去卷积问题提供了进一步的动力。 显示英文摘要

摘要： Via a simulation study we compare the finite sample performance of the deconvolution kernel density estimator in the supersmooth deconvolution problem to its asymptotic behaviour predicted by two asymptotic normality theorems. Our results indicate that for lower noise levels and moderate sample sizes the match between the asymptotic theory and the finite sample performance of the estimator is not satisfactory. On the other hand we show that the two approaches produce reasonably close results for higher noise levels. These observations in turn provide additional motivation for the study of deconvolution problems under the assumption that the error term variance $\sigma^2\to 0$ as the sample size $n\to\infty.$