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Unformatted text preview: 2 2 2 1 2 ( ) [ ( ) ( )]/ 4 ( ) / 4 / 2 Var X Var X Var X = + = + = 2 2 2 1 2 ( ) [ ( ) 9 ( )]/16 ( 9 ) /16 5 /8 Var Y Var X Var X = + = + = 2 2 2 1 2 ( ) [ ( ) 4 ( ) / 9 ( 4 ) / 9 5 / 9 Var Z Var X Var X = + = + = Hence, X is the most efficient estimator since ( ) ( ) ( ) Var X Var Z Var Y < < . Note that 1 2 ( )/ 2 X X X X = + = , then, 2 2 ( ) ( ) / / 2 Var X Var X n = = = . 26. Relative efficiency of X with respect to Y = ( ) / ( ) Var Y Var X = (5 2 / 8) / ( 2 / 2) = 5 / 4 = 1.25 Relative efficiency of X with respect to Z = ( ) / ( ) Var Z Var X = (5 2 / 9) / ( 2 / 2) =10 / 9 = 1.11...
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 Spring '08
 YILMAZ

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