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# Re: st: normality test using the over identifying moment conditions

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: normality test using the over identifying moment conditions Date Thu, 31 Jan 2013 12:30:44 +0000

```There is no mention here of what command you are using. With this kind
of data the number of values is usually so large that any test will
produce results significant at conventional levels, i.e. normality
will be rejected even for trivial deviations from normality.

A search of the archives will show many posts explaining why tests of
normality are usually a bad idea.

Nick

On Thu, Jan 31, 2013 at 12:21 PM, Usman Gilani <u.gilani@icloud.com> wrote:
> Hi,
> I'm trying to interpret the following results, with respect to "normality
> test using the over identifying moment conditions"
>
> where returns have normal distribution
> with parameter mu,sd
> and i have 4 moment conditions
>
>>E[r-mu/sd]=0
>
>>E[(r-mu)^2/sd-1]=0
>
>>E[(r-mu)^3/sd^3]=0
>
>>E[(r-mu)^4/sd^4-3]=0
>
> output..
> gel(g = g, x = returns, tet0 = c(f3\$estimate[1], f3\$estimate[2]))
>
> Type of GEL:  EL
>
> Coefficients:
>               Estimate  Std. Error     t value   Pr(>|t|)
> mean  -0.01168   0.05614    -0.20805   0.83519
> sd         1.77591   0.03965    44.79218   0.00000
>
> Lambdas:
>                         Estimate   Std. Error  t value    Pr(>|t|)
> Lambda[1]   -0.09743    0.03912    -2.49028    0.01276
> Lambda[2]    0.65728    0.02443    26.90505    0.00000
> Lambda[3]    0.03247    0.01304     2.48961    0.01279
> Lambda[4]   -0.10954    0.00407   -26.90423    0.00000
>
>  Over-identifying restrictions tests: degrees of freedom is 2
>                      statistics     p-value
> LR test   2.3341e+02   2.0730e-51
> LM test   7.2417e+02   5.5954e-158
> J test      7.2417e+02    5.5954e-158
>
> Convergence code for the coefficients:  0
>
> Convergence code for the lambdas:  0
>
>
> does the J-test p-value rejecting the null E[g(theta,x)]=0, and which moment
> condition is true under normality
>
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```