The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.stat.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: A pertinent/impertinent question. . .
Replies: 8   Last Post: Nov 13, 2013 4:02 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ] Topics: [ Previous | Next ]
Luis A. Afonso

Posts: 4,758
From: LIsbon (Portugal)
Registered: 2/16/05
Re: A pertinent/impertinent question. . .
Posted: Nov 3, 2013 7:54 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Towards asymptotic distribution functions

Since, as was yet found in literature, that either U and V,
_____U= n/6* [m3/(m2^1.5)]^2_____(a1)
_____V= n/24*[m4/(m2^2 - 3]^2____(a2)
JB=U+V, does not follow each one, for moderated size samples, a chi squared 1 degree of freedom (df) Distribution, it was thought that to use exact quantiles of JB statistics vs. the sizes, n, would solve the problem rigorously.
However, clearly, this is not the case: each estimation formula have its own speed to became stable and equal each other.

_A)__ similarity asymptotic
___n=4000/40´000____(2 experiments)
The formulas (a1),(a2) above concerns the LM version[1].


Note: the quantiles (from .4 to .9) seems not to differ for the two r.v.. Furthermore should be compared with those from the Chi-square: 0.275, 0.455, 0.708, 1.074, 1.642, 2.706.
It is good practice do not use the JB test for samples shorter than 4000. Otherwise the contributions U and V to the total are quite unbalanced resulting that we are testing the sample problem not fairly regarding both parameters.

B) In what concerns the ALM procedure [1] it was not expected differences for large samples because it not modifies the estimates.


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

Luis A. Afonso

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.