AMDA-2008-Session 4 - The Bootstrap Introduction The...

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The Bootstrap
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Introduction The bootstrap is a computational method for obtaining estimate of standard error of an estimator. It can also be used for obtaining confidence intervals The Bootstrap technique was invented by B. Efron in 1979.
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Bootstrap Idea . simulation using ) ( V e Approximat : 2 Step ) ( V with ) ( V Estimate : 1 Step : steps two has idea bootstrap The . T of variance the be ) (T V and statistic a be ) ,..., ( T Let n n F ˆ F ˆ F n n F 1 n n n n n T T T X X g =
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Note n X X n T n T X T n i i n n n n = - = = = 1 2 F ˆ 2 F n F ˆ ) ( 1 ) ( V hence, ; ) ( V then T if example For form. simple a in expressed be can ) ( V if needed not is 2 Step n n σ
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Law of Large Numbers )) ( ( ) ( n 1 Then, . h function any for ),. .. h(X ), h(X is so then variables random iid of sequence a be ,... , X if that Note : Corollary X Then . ) (X E with variables random iid of sequence a be ,... , X Let 1 2 1 2 1 n i F 2 1 X h E X h X X n i P i P = → → = μ
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This note was uploaded on 05/07/2009 for the course FIN AMDA taught by Professor Proflaha during the Spring '09 term at Indian Institute Of Management, Ahmedabad.

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AMDA-2008-Session 4 - The Bootstrap Introduction The...

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