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Ozean Journal of Applied Sciences 4(4), 2011
1. Calculating one stage shrinkage estimator using a fixed shrinkage function as the following:
~
( ˆ
~ K 0
… (9)
K ( ˆ
… (10)
Set:
0 )
0 )
ˆ ~ N [ ,
Var(
ˆ)]
ˆ ~ N [ , Var(
ˆ) ]
0
For calculating the bias of estimated shrinkage ~ :
~
~
Bias ( ) E ( )
~
ˆ
Bias ( ) E [ K(
0 ) 0 ]
~
ˆ
Bias ( ) K E(
0 ) E(
0
)
K ( ˆ ) ( ˆ) ˆ ( ) ( ˆ) ˆ
0 f d
0 f d
… (11)
1 ˆ 2
ˆ
( )
K ( ).
.
ˆ
0 Exp
d
2Var(
ˆ)
K
( )
K
2
V ( ˆ)
1 ˆ 2
( )
Exp
2
Var(
ˆ) 2Var
( ˆ)
0 d
( ˆ ).
ˆ
… (12)
ˆ 2
1
( )
Exp
2
Var ( ˆ)
2Var
( ˆ)
0 d
1 ˆ 2
( )
ˆ
( 0 ).
Exp
d
2
Var ( ˆ) 2Var
( ˆ)
… (13)
( ˆ ).
1 ˆ 2
( )
Exp d ˆ K
2
Var ( ˆ)
2Var
( ˆ)
1 ˆ 2
( )
Exp d ˆ
2
Var ( ˆ)
2Var
( ˆ)
ˆ 2
( )
Exp d ˆ
2Var
( ˆ)
...(15)
( ).
ˆ 2
( )
Exp d ˆ ...(14)
2Var
( ˆ)
1 ˆ 2
ˆ
( )
K ( ).
ˆ
Exp d
( K 1)
2
Var(
ˆ)
2Var
( ˆ)
0
( )
1
0
2
Var ( ˆ)
( )
0
ˆ
1
2
Var(
ˆ)
398