# Re: st: bootstrap estimation

 From Stas Kolenikov To statalist@hsphsun2.harvard.edu Subject Re: st: bootstrap estimation Date Mon, 27 Sep 2004 16:53:02 -0400

```So that's where the weird idea of implementing bootstrap through AR(1)
reported in the last Stata Journal comes from; the business research
community. Or am I the only one unhappy about that "Help Desk"
article? Of course there's a beauty of getting any results you want
from utilizing arbitrary assumptions about the data generating
processes (what if it is not an AR(1), but ARMA(3,5), or some sort of
threshold AR? what if it is not a stationary AR(1), but a random walk,
or something fractionally cointegrated? Or something that has a ARCH
structure to it?), but generally implementing bootstrap even for
simplest regression models reqiures several levels of assumptions
(correct model specification, iid residuals, etc.). Doing this over
time series is hopeless to me.

Sorry for my malicious answer, I think this is a totally wrong idea to pursue.

Could you also please explain what is meant by the small sample bias?

And, finally, the bootstrap methods are used to estimate the standard
errors, not the coefficients. And the only theoretically solid
justification for the bootstrap I know of comes from asymptotic
Edgeworth expansions.

Stas

On Mon, 27 Sep 2004 16:22:19 -0300, Raquel Oliveira
<raquel@labfin.com.br> wrote:
> I need to implement a bootstrap procedure to correctly estimate the coefficients of a regression that is subject to small-sample bias. The regression is: Y = a + bX + e  The series of Ys contains annual data.
>
> Following the procedure described in Eleswarapu and Reinganum (Journal of Business, Apr. 2004), I need to estimate an AR(1) of the independent variable X, save the residuals and the estimates of the coefficients. Then I need to randomize, with replacement, the series of residuals. I can then create a series of pseudo-X, using the randomized series of residuals along with the coefficients estimated in the AR(1). The starting values for X(-1) are randomly chosen from the actual data.
>
> On the other hand, I also need to randomize a series of monthly Ys, with replacement, and compute a series of pseudo-Y, which are annual, from the monthly randomized Ys.
>
> Finally, I need to bootstrap the regression Pseudo-Y = a + bPseudo-X + e. This last procedure I know how to implement. It is the creation of the randomized series of residuals, the pseudo-X and pseudo-Y that I haven't been able to do.
>
> Thank you for your attention.
>
> Best regards,
> Raquel Oliveira.
>
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--
Stas Kolenikov
http://stas.kolenikov.name
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```