误差方差的混合估计和有偏估计

The Mixed Estimate and Biased Estimate of Error Variance

本文利用“离差—均值对应”方法,研究了线性模型(y,X,σ~2I)在扩大样本下误差方差的混合估计方法,并证明了其混合估计优于LS估计。进一步,讨论了误差方差的岭估计及其优良性,证明了它是误差方差的可容许估计。

This paper discusses estimates of error variance σ~2 in Iinear model (y,x,σ~2I) by introducing 'dispersion-mean correspondence'. The mixed estimate is presented on the condition of expanding sample date and is superior to is estimate of error variance. Furthermore, ridge estimate is given, it is shown that ridge estimate is uniformly superior to is estimate of error variance and is admissible estimate under the suitable condition.