论文标题
在泊松和高斯实验之间的LE凸轮距离以及Szasz估计器的渐近特性之间
On the Le Cam distance between Poisson and Gaussian experiments and the asymptotic properties of Szasz estimators
论文作者
论文摘要
在本文中，我们仅使用基本方法（Taylor Expantions和Stirling的公式），证明了泊松分布与高斯分布的比率具有相同的平均值和方差的比率。然后，我们将结果应用于Poisson和Gaussian实验之间的LE CAM距离上的上限，该实验的完整证明了Pollard（2010）的未发表的一组讲义中提供的草图，后者使用了另一种方法。我们还使用局部极限定理来得出伯恩斯坦C.D.F.方差的渐近学。和密度估计器在正期为正（也称为Szasz估计器）上。附录中解决了由于Leblanc（2012）的引理2（iv）中错误估计而导致的文献中错误的传播。
In this paper, we prove a local limit theorem for the ratio of the Poisson distribution to the Gaussian distribution with the same mean and variance, using only elementary methods (Taylor expansions and Stirling's formula). We then apply the result to derive an upper bound on the Le Cam distance between Poisson and Gaussian experiments, which gives a complete proof of the sketch provided in the unpublished set of lecture notes by Pollard (2010), who uses a different approach. We also use the local limit theorem to derive the asymptotics of the variance for Bernstein c.d.f. and density estimators with Poisson weights on the positive half-line (also called Szasz estimators). The propagation of errors in the literature due to the incorrect estimate in Lemma 2 (iv) of Leblanc (2012) is addressed in the Appendix.
