变换核估计和迭代算法

THE TRANSFORMED KERNEL ESTIMATION AND ITERATIVE ALGORITHM

设X_1,X_2,…,X_n为独立同分布的随机变量,其密度函数为f(x),该函数有较陡的起始部分和较长的尾部,如对数正态和威布尔密度函数等。考虑一个变换T:Y_i=T(X_i),使得Y_i的密度函数g(y)具有较小的估计误差。这样,f(x)可用T′(x)g(T(X))来估计。本文给出了变换核估计的迭代算法。并讨论了估计的特性,蒙特卡罗方法模拟的结果表明变换核估计对对数正态及威布尔分布的密度函数的估计是合适的。

Let X1,…, Xn be i.i.d. random with density function/(x), which has the shape of a steep head and a heave tail such as log-normal and Weibull density function. Consider a transformation T:Yι=T(Xι), where Yi obey a density function g(y) which has a minimum error of estimate. The estimate f(x) can be obtained by f(x)= T'(x)g(T(x)). In this paper we present a iterative algorithm of the transformed kernel estimate and discuss the performance of estimate. A Monte Carlo simulations show that the transformed kernel estimate is suitable for the estimate of log-normal and Weibull density function.