Buhlmann-Straub信度模型的估计与检验

Estimating and testing parameter for Buhlmann-Straub model

研究了Buhlmann-Straub信度模型的参数估计和随机效应的检验,以及它们的统计性质.参数估计采用两步估计法,用F检验对随机效应进行检验.在两步估计法中,利用正交变换得到了总平均的估计,然后采用拟合常数法得到了方差的估计,并证明了该估计是无偏估计.通过残差平方和构造了F检验统计量对是否有随机效应进行检验,并得出了检验的势函数是检验方差的增函数.最后将估计和检验的方法应用到实例中,得到了较好的效果.

In this Paper, the parameters and random effect of Buhlmann-Straub credibility model were researched. Two-stage estimate was used to estimate the parameter and F-test was used to test the random effect. In two-stage estimate, used orthogonal transformation to estimate aggregate average and fitting constants method to estimate variance which was unbiased. Used regression sum of squares to get the F-test statistic in order to test the random effect, the power of the test is increasing function of the test variance. AT last, the methods were used in a example that get good result.