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Re: st: Quantile Regression


From   Robert Davidson <rhd773@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Quantile Regression
Date   Tue, 2 Oct 2012 23:15:37 -0400

Thank you for the responses.

I am performing the same number of bootstrap replicates in each model
and I did not receive any messages that any of the quantiles failed to
converge.  I will check into setting the same random seed before each
command; I did not set anything before running either command so
perhaps that is the issue.  One thing I should mention is that the
standard errors in some cases were dramatically different, not just a
little bit off and that is what surprised me given the number of
observations I have.

I will take a look at Koenker's book as well.  It would help a great
deal to find a faster way to estimate these models.

In case anyone has suggestions based on the model itself, I have a
large sample of firm-level stock returns and a series of variables
related to the firm's CEO.  I am trying to estimate whether certain
'types' of CEOs are over or under represented at different quantiles
of stock returns.  I can see a pattern by plotting a simple histogram,
but want a stronger indicator of the relation and magnitude.

Thanks again,
Rob

On Tue, Oct 2, 2012 at 10:12 PM, JVerkuilen (Gmail)
<jvverkuilen@gmail.com> wrote:
> On Tue, Oct 2, 2012 at 7:31 PM, Steve Samuels <sjsamuels@gmail.com> wrote:
>>
>> Without details (see FAQ 3.3 first sentence), we can only guess. This
>> could happen if 1) you did not set the same random seed before each
>> -sqreg- and -bsqreg- command; 2) the number of bootstrap replicates
>> differed between -sqreg- and -bsqreg- runs; or 3) -sqreg-  does not
>> rejects replicates in which convergence failed for any quantile.
>
> If the standard errors are different it's no great surprise if you're
> running bootstrap. All the stuff said makes sense. Check on a known
> dataset (such as auto) and fix the seed.
>
>
>
>> By the way, the manual states that -sqreg- is faster than -bsqreg-.
>
> I believe that computationally there are some speedups due to the fact
> that the linear program can be solved for one and simply updated to
> get the rest of the quantiles, but I could be mistaken. Roger
> Koenker's book (Quantile Regression, Oxford University Press, 2006)
> discusses computation in detail. Also there are analytic options to
> bootstrapping that might be much faster. -qreg- generates standard
> errors analytically using a weighting matrix and density estimator of
> the residuals.
>
> . sysuse auto
> . qreg price mpg
>
> Median regression                                    Number of obs =        74
>   Raw sum of deviations   142205 (about 4934)
>   Min sum of deviations 129521.7                     Pseudo R2     =    0.0892
>
> ------------------------------------------------------------------------------
>        price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>          mpg |  -135.6667   67.26576    -2.02   0.047    -269.7585   -1.574816
>        _cons |   8088.667   1483.808     5.45   0.000     5130.749    11046.58
> ------------------------------------------------------------------------------
>
>
>
>
>
> . bsqreg price mpg, reps(999)              *note that bsqreg defaults
> to 20!?!?!?!
>
> Median regression, bootstrap(999) SEs                Number of obs =        74
>   Raw sum of deviations   142205 (about 4934)
>   Min sum of deviations 129521.7                     Pseudo R2     =    0.0892
>
> ------------------------------------------------------------------------------
>        price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>          mpg |  -135.6667   35.63527    -3.81   0.000    -206.7043   -64.62906
>        _cons |   8088.667   889.0486     9.10   0.000     6316.381    9860.953
> ------------------------------------------------------------------------------
>
>
> In this case the standard errors are markedly different and playing
> with the different methods in -qreg- gives quite different values, but
> I don't really know enough to be able to comment on why. I am inclined
> to trust the bootstrapped ones because this problem has a rather small
> N.
>
> I suspect that it is very slow on a huge problem though, given that it
> needs to sort the residuals. Koenker did a good deal of work on
> alternatives such as inverting a test of some sort; I think the R
> implementation of quantile regression has this. Again see his book.
>
>
>
>> I've never had the luxury of having so many observations to analyze. I
>> imagine that almost every simple model can be rejected, so that model
>> building and validation are real challenges.
>
> Randomly subsample and do a real cross validation?
>
> Jay
> --
> JVVerkuilen, PhD
> jvverkuilen@gmail.com
>
> "Out beyond ideas of wrong-doing and right-doing there is a field.
> I'll meet you there. When the soul lies down in that grass the world
> is too full to talk about." ---Rumi
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