一类最优无偏估计及其应用

A CLASS OF BEST UNBIASED ESTIMATE, AND ITS APPLICATIONS

推广了定理1〔1〕的结果得到定理2及其推论,并说明其应用。

In this paper,the theory l(Best Linear Un-biased Estimate ) is expanded, and obtain theory 2: Suppose that T1T2……Tk are UnbiasedEstimates of Estimable function 9 (θ) , and the Covariances cov (TiTj) = cij <∞.If T = ∑biTi is the Best Unbiased Estimator of g(θ), for the linear combination class of Ti ( i = 1 .2…k ) , then it must be bi = α(ik+i) , i=1.2…k.In which α(ik+1) is the element of the inverse matrix A(-1) of matrix A= (cjj).Finally, as application of the result, the estimate of o2 in Analysis of Variance is discused.