一个重要统计量的鞍点逼近

Saddlepoint Approximation to an Important Statistic

在统计中,卡方分布是一个非常重要的分布,不只因为它本身是一种和正态分布密切相关的分布类型,更重要的是在假设检验中,很多统计量的渐近分布是卡方分布.事实上,独立的卡方分布随机变量的线性组合的分布作为一类分布也是十分重要的,但是大部分情况下无法简单得到其密度函数形式.本文运用三种逼近技术来近似得到这类分布的密度函数.特别是鞍点逼近的应用,提供了一种非常好的密度函数逼近方法.

As is well known, chi-square distribution is a very important distribution in statistics. Besides the close relationship with normal distribution, what＇s more significant is that numerous statistics＇ asymptotic distribution is chi-square distribution in hypothesis test. In fact, the distribution of linear combination of independent chi-square random variables is also an important class of distribution. Unfortunately, we can not get the density function in most cases. We apply three approximation techniques to obtain the density function approximatively. In particular, the application of saddlepoint approximation provides an effective density approximation method.