On the estimation of parametric density functions
On the estimation of parametric density functions
复制标题
关于参数密度函数的估计
DOI：
10.1093/biomet/67.2.505
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发表时间：
1980
期刊：
影响因子：
2.7
通讯作者：
V. Ng
中科院分区：
文献类型：
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作者：
V. Ng
给出了统计模型中参数密度函数在变换群下不变的最佳不变估计。对于基于信息度量的拟合优度标准，估计是最好的。讨论了用数据x估计参数密度函数p(Yi0).设r(Yi0)是p(Yi0)的估计，考虑基于Kullback&Liebler(1951)的信息度量的拟合优度准则，r(Yix)与p(Yi0)的偏差为J=p‘(XI0)dxp(Y0)log{p(Yi0)/r(Yix)}dy，其中p‘是数据x的密度函数。最小化J并且在一组变换下不变的估计称为最佳不变。这里我们推广了Murray(1977)的结果，他得到了多元正态密度函数的最佳不变估计。假设假设了一类参数密度函数{p(Y I 0)：0 E E)，y E Y
SUMMARY The best invariant estimate of the parametric density function in statistical models invariant under a transformation group is derived. The estimate is best with respect to a goodness-of-fit criterion based on an informa,tion measure. We are concerned with the estimation of a parametric density function p(y I 0) using data x. Let r(y Ix) be an estimate of p(y I 0) and consider the goodness-of-fit criterion based on an information measure of Kullback & Liebler (1951), the deviation of r(y I x) from p(y I 0) being J= p'(xI0)dx p(y 0) log {p(y I 0)/r(y Ix)}dy, where p' is the density function of the data x. An estimate that minimizes J and is invariant under a group of transformations is said to be best invariant. Here we generalize the result of Murray (1977), who derived the best invariant estimate of the multivariate normal density function. Suppose that a class of parametric density functions {p(y I 0): 0 E E), y E Y} is postulated