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Luis A. Afonso
Posts:
4,613
From:
LIsbon (Portugal)
Registered:
2/16/05


Bootstrap: Skewness and Kurtosis, normal data
Posted:
Nov 20, 2013 5:22 PM


Bootstrap: Skewness and Kurtosis, normal data
A rather futile exercise, again. . .
The *horrific* Principles about Bsampling:
__1__The Bprocedure adds more information about the Population it derived than that the nsized Source sample itself provides. __2__It is able to reconstruct the Population. __3__In the Population each sample item have the same probability to occur, therefore we can safely to sample from the Source with replacement with probability 1/n. __4__Repeated values (continuous Distribution) are as likewise than different ones. __5__The set of real samples could be perfectly represented with the n items the Source have. _____________
The Exercise:
One normal (standard) item X( ) is simulated through the BoxMuller model. Repeating m=2000 times the Source is built and the Skewness and Kurtosis, S0, K0. The Source is bootstrapped, S and K evaluated.
Results: ______ p(S0 > S) = 0.281 to 0.296 _______Z = 21.9 to 20.0 ______ p(K0 > K) = 0.562 to 0.584 _______Z = 5.6 to 7.6
Z tests both very significant: the Bootstrap data is not conformable with source ones. As expected . . .
Luis A. Afonso



