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Topic: Just for fun
Replies: 2   Last Post: Jan 9, 2014 4:16 PM

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Luis A. Afonso

Posts: 4,518
From: LIsbon (Portugal)
Registered: 2/16/05
Just for fun
Posted: Dec 30, 2013 3:01 PM
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Just for fun

Noting that both U= (n/6)*S^2 and V= n/24*(K-3)^2, JB=U(S) + V(k), do depend from the second central moment is intuitively obvious to assume that the two Jarque-Bera test statistics summands are strongly correlated. In order to try to destroy this feature we (just for fun) *split* the sample into two halves: firstly estimating the the third and the second then, the fourth and a fresh second moment. Note that in this instance we do not really split a sample, rather we *draw* (simulate) other sample.

Results:

We simulate the two-sample way, n= 20 + 20 <APART> and the current way <JBcurrnt>, n= 40; the Quantiles Q from 0.05 to 0.95 are shown below.



___n=___20+20__40__________20+20__40__
___Q__________________Q______________

__0.05___0.07__0.10____0.10___0.15__0.20_
__0.15___0.23__0.30____0.20___0.31__0.39_
__0.25___0.39__0.49____0.30___0.47__0.59_
__0.35___0.56__0.69____0.40___0.65__0.79_
__0.45___0.74__0.90____0.50___0.84__1.01_
__0.55___0.96__1.13____0.60___1.08__1.26_
__0.65___1.22__1.40____0.70___1.38__1.56_
__0.75___1.58__1.76____0.80___1.85__2.00_
__0.85___2.22__2.36____0.90___2.82__3.00_
__0.95___4.02__4.78____

Note that the values are quite similar, the present way only a little less disperse than the classic procedure, see:

arXiv:math/0509423v1 [math.ST] 19 Sep 2005


Luis A. Afonso



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