where 
Y= {o; (2.13) 
and a'/ is an element of inverse matrix, so that 
1 
JDERedoy 5S 6 6.0 Xn) exp -5{e-#) D1 @-m)| . (2.14) 
1 
= (27)"/2A1/2 
2.2 PROPERTIES REQUIRED FOR ESTIMATOR 
The following properties are required for the estimator of some statistical value. 
2.2.1 Unbiasedness 
As the number of samples n tends toward infinity, for the estimator 6 of real 6, 
bias) = {E() es 6| 5 (0), 3 (2.15) 
22.2 High Relative Efficiency 
If we suppose that both estimators 6,,6, are unbiased, then the higher the 
rel. effic. = var. (6;)/var. (62) (2.16) 
is, the better estimator 6, is than @,. 
2.2.3 Small Mean Square Error 
Mean square error is defined as 
M*6) = E[(@ - 6)"] 
= A|{6 z E(6)| + {E(6) e 6} 
= A|{6 as z6)} | + {E(6) bs a" + 2{E(6) - o\zI6 ~ E(6)] 
= var. (6) + b%(6), (2.17) 
which should be small. When M2(6 ;) < M(6>), we adopt 6 as better than 6. 
