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

 From Usman Gilani To statalist@hsphsun2.harvard.edu Subject Re: st: normality test using the over identifying moment conditions Date Thu, 31 Jan 2013 13:06:56 +0000

```Dear Nick,

the dataset has 1000 obs.
and I'm not using Stata this output is from R
i tried to run this test in stata but cause of limited stata knowledge I couldn't do it.

please tell me how can i do gmm test with following moment conditions in stata

thanks

best

Gilani
On 31 Jan 2013, at 12:30, Nick Cox <njcoxstata@gmail.com> wrote:

> 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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```