论文标题
七个不对称核的研究估计累积分布函数
A study of seven asymmetric kernels for the estimation of cumulative distribution functions
论文作者
论文摘要
在Mombeni等。 （2019年），引入了Birnbaum-Saunders和Weibull内核估计器，以估算在半行$ [0，\ infty）$上支持的累积分配功能（C.D.F.S）。他们是在C.D.F.的背景下使用不对称内核的第一位作者。估计。显示它们的估计器比传统方法（例如基本内核方法和Tenreiro（2013）的边界修改版本）的数值表现更好。在本文中，我们通过引入五个新的不对称核C.D.F.来补充他们的研究。估计量，即伽马，反伽马，对数正态，高斯和倒数逆高斯核C.D.F.估计器。对于这五个新的估计量，我们证明了渐近正态性，并且发现以下数量的渐近表达式：偏差，方差，平均平方误差和平均综合平方误差。然后，一项数值研究比较了五个新的C.D.F.的性能。针对传统方法的估计值以及Birnbaum-Saunders和Weibull内核C.D.F. Mombeni等人的估计器。 （2019）。通过使用相同的实验设计，我们表明logNormalal和birnbaum-Saunders内核C.D.F.估计器的总体表现最好，而其他不对称内核估计器有时会更好，但至少在边界内核方法上始终具有竞争力。
In Mombeni et al. (2019), Birnbaum-Saunders and Weibull kernel estimators were introduced for the estimation of cumulative distribution functions (c.d.f.s) supported on the half-line $[0,\infty)$. They were the first authors to use asymmetric kernels in the context of c.d.f. estimation. Their estimators were shown to perform better numerically than traditional methods such as the basic kernel method and the boundary modified version from Tenreiro (2013). In the present paper, we complement their study by introducing five new asymmetric kernel c.d.f. estimators, namely the Gamma, inverse Gamma, lognormal, inverse Gaussian and reciprocal inverse Gaussian kernel c.d.f. estimators. For these five new estimators, we prove the asymptotic normality and we find asymptotic expressions for the following quantities: bias, variance, mean squared error and mean integrated squared error. A numerical study then compares the performance of the five new c.d.f. estimators against traditional methods and the Birnbaum-Saunders and Weibull kernel c.d.f. estimators from Mombeni et al. (2019). By using the same experimental design, we show that the lognormal and Birnbaum-Saunders kernel c.d.f. estimators perform the best overall, while the other asymmetric kernel estimators are sometimes better but always at least competitive against the boundary kernel method.
