Asymptotic Methods in Statistical Inference - Statistics Centre

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• Example 4. In the same framework as the previous
example, suppose instead that
( ) = |bias of 2 |
∙ = ¯ − 1
2¸
¯
− 2¯¯¯¯
= 2 ( )
Then (18.2) and (18.3) are trivially satisfied, with
= ( ) = 0, hence the bootstrap works. It has
error
= ( ˆ ) − ( )
= 2 ( ˆ ) − 2 ( )
= 2 − 2 ( )
= ( −32 )
since √ ³ 2 − 2´ = (1). In contrast, the
error incurred by using ³ ˆ ´
= =0toestimate
( ) is of a larger order:
0 = ³ ˆ ´
− ( )
= − 2 ( )
= ( −1 )