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# Re: st: RE: A math question

 From Yuval Arbel To statalist@hsphsun2.harvard.edu Subject Re: st: RE: A math question Date Fri, 21 Dec 2012 07:52:37 -0800

```CJ, I don't know if this is your intention, but it might be of
assistance to take a look at econometric textbooks regarding how to
derive LAD (Least Absolute Deviations) and Quantile regression
estimators.

As Johnston and Dinardo put it: "As it turns out the LAD estimator
correspond to median regression, which is consistent for beta
because..." (page 445). Moreover, this system carries out the payoff
of median regression, which is unaffected by extreme values (unlike
the simple OLS).

The full reference is:

Johnston and Dinardo: Econometric Methods, Fourth Edition (1997)

On Fri, Dec 21, 2012 at 7:27 AM, Feiveson, Alan H. (JSC-SK311)
<alan.h.feiveson@nasa.gov> wrote:
> CJ -The median is one number, not a function - so it doesn't make sense to talk about differentiating it.
>
>
> If you mean what is the derivative of abs(x^3) with respect to x, it would be 3*x^2, because the derivative for x < 0 is the same as for x > 0 = 3*x^2.
>
>
>
> Al Feiveson
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of CJ Lan
> Sent: Friday, December 21, 2012 9:13 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: A math question
>
> Folks,
>
> I am not sure if this is an appropriate question but I am hoping someone wh= o knows the answer do not mind rendering her/his hands.
>
> What is the derivative of the median(abs(x^3)) with respect to x ?
>
> Thank you.
>
> CJ
>
>
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--
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: yuval.arbel@carmel.ac.il
e-mail2: yuval.arbel@gmail.com

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```

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