Jarque-Bera test: confidence intervals for normal
data, 2

RAW RESULTS
_SIZE_________5%___________1%______
__10______2.54__2.53_____5.72___5.70__
__15______3.30__3.29_____8.26___8.18__
__20______3.81__3.79_____9.73___9.66__
__25______4.16__4.16____10.78__10.74__
__30______4.40__4.41____11.33__11.27__
__35______4.57__4.59____11.67__11.80__
__40______4.74__4.77____11.95__12.01__
__45______4.86__4.88____12.29__12.19__
__50______4.95__4.95____12.36__12.46__

(1 million of samples, size N, 2 times, for each
sample size). Remembering that the theoretical,
asymptotical, Chi-squared, 2 DF, are 5.991 (5%) and
9.210 (1%) this calculation’s utility seems
unquestionable.

________licas (Luis A. Afonso)

Jarque-Bera test: confidence intervals for normal
data, 3


Jack L. Tomsky KNOWS NOTHING about it is saying.


_____licas (Luis A. Afonso)

Jarque-Bera test: confidence intervals for normal
data, 3

After *smoothing*


__V.C.__5% Significance

__10__2.54____11__2.71__
__12__2.87____13__3.02__
__14__3.16____15__3.29__
__16__3.41____17__3.52__
__18__3.62____19__3.72__
__20__3.81____21__3.89__
__22__3.96____23__4.03__
__24__4.09____25__4.15__
__26__4.21____27__4.26__
__28__4.31____29__4.36__
__30__4.40____31__4.44__
__32__4.48____33__4.52__
__34__4.56____35__4.59__
__36__4.62____37__4.66__
__38__4.69____39__4.72__
__40__4.74____41__4.77__
__42__4.80____43__4.82__
__44__4.85____45__4.87__
__46__4.89____47__4.91__
__48__4.92____49__4.94__
__50__4.95_____________

For example H0 is not rejected (at 5% significance
level) if a sample of size 50 has a JB equal or less
than 4.95.


________licas (Luis A. Afonso)

Jack Tomsky wrote

*** What you've described is a statistical test for
the composite hypothesis of normality. But what is
the parameter that the confidence interval pertains
to? In other words, given a sample of size N, what
is your unknown parameter and what is your confidence
interval? That's what we were promised by your
thread title. ***
_______________________________________________

My response

This is at least the second time that I stress this
point.

All GOF (goodness of fit ) test are built in these
terms
__1__The null hypotheses H0 is: the sample could
eventually be drawn from the Distribution N? (Here,
the normal distribution).
__2__If so, I am free to get a *sample statistics*,
W, such that I find out the *cumulative probability*
F(W) for the critical values.
__3__Considering the Jarque-Bera test, W is the same
whatever the NORMAL mean and variance are. The trick
is
____a) using the CENTRL moments
____b) using as for the SKEWNESS, S, as for the
KURTOSIS, K, values that are reduced (division by
variance raised to 3/2, square of the variance,
respectively).

Because W is always positive we DEFINE the acceptance
interval as [0, U: F(U) = 1-alpha]. This acceptance
interval is such that if the test provides a value W0
= U we are sure (at the significance level alpha)
that H0 COULD NOT BE REJECTED: there are not
sufficient evidence to do so.
On contrary if W0 > U we cannot accept H0, there ARE
SUFFICIENT EVIDENCE that the sample was not drawn
from a normal distribution (at the significance level
alpha). ________________________________

The Jack´s INSISTENCE in deny the legitimacy of a GOF
test (like Jarque-Bera) only because (I quote):
*** But what is the parameter that the confidence
interval pertains to?***
clearly shows that Tomsk, besides unlearned in
Hypotheses test, is prone to careless statements, and
immensely STUPID.
________________________________

________licas (Luis A. Afonso)

As I did mention all the problematics concerning the
Jarque- Bera test for finite sample size is clearly
depicted in the Steve Lawford´s paper. I simply
followed his procedure (Monte Carlo simulations) in
order to define the acceptance intervals for the two
ordinary significance levels, 5% and 1%. IMO my
values are in agreement with the quantiles of Fig. 2,
qhat 0.95.in function of the sample sizes. (0.99 ones
are absent). I invite the Readers to consult it
______Finite-sample quantiles of the Jarque-Bera
test.
______Steve Lawford (first draft Feb. 2004).

AFTER reading it I am really pleased to have a
learned discussion on this matter. NOT BEFORE.
___Mouth-dance, NO, thank you.

_________licas (Luis A. Afonso)

Jack Tomsky wrote

*** What you've described is a statistical test for
the composite hypothesis of normality. But what is
the parameter that the confidence interval pertains
to? In other words, given a sample of size N, what
is your unknown parameter and what is your confidence
interval? That's what we were promised by your
thread title. ***
_______________________________________________

My response

This is at least the second time that I stress this
point.

All GOF (goodness of fit ) test are built in these
terms
__1__The null hypotheses H0 is: the sample could
eventually be drawn from the Distribution N? (Here,
the normal distribution).
__2__If so, I am free to get a *sample statistics*,
W, such that I find out the *cumulative probability*
C(W) for the critical values.
__3__Considering the Jarque-Bera test, W is the same
whatever the NORMAL mean and variance are. The trick
is
____a) using the CENTRL moments
____b) using as for the SKEWNESS, S, as for the
KURTOSIS, K, values that are reduced (division by
variance raised to 3/2, square of the variance,
respectively).

Because W is always positive we DEFINE the acceptance
interval as [0, U: p(C(W) = 1-alpha]. This acceptance
interval is such that if the test provides a value W0
= U we are sure (at the significance level alpha)
that H0 COULD NOT BE REJECTED: there are not
sufficient evidence to do so.
On contrary if W0 > U we cannot accept H0, there ARE
SUFFICIENT EVIDENCE that the sample was not drawn
from a normal distribution (at the significance level
alpha). ________________________________

The Jack´s INSISTENCE in deny the legitimacy of a GOF
test (like Jarque-Bera) only because (I quote):
*** But what is the parameter that the confidence
interval pertains to?***
clearly shows that Tomsk, besides unlearned in
Hypotheses test, is prone to careless statements, and
immensely STUPID.
________________________________

________licas (Luis A. Afonso)

I suppose I got what Jack problem is.


My goal is to test he null Hypotheses
____H0 : Could be the sample from a Normal
Distribution? , against
____Ha : The distribution is not Normal.

For this I found
a)************ an ACCEPTANCE interval for H0 ******
which is bounded by a no-null,
b) ************* CRITICAL VALUE****************
which is completed by a
c) ***** NO-ACCEPTANCE (rejection) INTERVAL*****
to which is attached to a
d) *** SIGNIFICANCE LEVEL (alpha) PROBABILITY ***

What was my *error* ?
_________I CALLED a) confidence interval
!!!!!!!!!!!!!

All the usefulness of typically empty and Byzantine
ACADEMIC minds is to shout: HORROR ! , only for
parameters is allowed to speak about confidence
intervals!!!!!!!!!!

REALLY…

______________licas (Luis A. Afonso)

Jack Tomsky wrote:

*** Congratulations, Luis, you finally got it. Now I
suppose you won't treat acceptance intervals and
confidence intervals as synonyms any longer. Jack
***


… which s equivalent of do not discern a difference
between IDENTICAL
TWINS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
__________IMBECILE.

_________licas (Luis A. Afonso)