[Gretl-users] Bootstrap news

[Andreas Karlsson]

I have tested the new bootstrap analysis for OLS. It is VERY good, and very
useful. Thanks a lot.

The only thing I am missing is the possibility to save the values of the samling
distribution as a new variable in the data set. This could be useful if one e.g.
want to plot a histogram of this distribution (the kernel density estimation
plot obtained from the bootstrap menu entry is nice, but I prefer histograms).

Further, if the bootstrap method could be implemented for the Least Absolute
Deviation regression method too, I would find this very useful.

Med vänliga hälsningar / Best regards
Andreas Karlsson

cottrell at wfu.edu skrev 2007-03-29 04:55:03 :

> Andreas K suggested a short while ago that gretl should offer 
> various bootstrap options via the graphical interface (GUI).  I 
> agreed at the time that this was a good idea.  Here's a note on 
> progress so far (in CVS, and the current gretl snapshot for Windows).
> 
> First, the limitation: all of the following new stuff applies only 
> to single-equation models estimated via OLS.  (Though please note 
> that we already offer bootstrapped confidence intervals for impulse 
> response functions in relation to VARs.)
> 
> When you estimate a model via OLS in the GUI, the model viewer 
> window has a menu bar, including items labeled "Analysis" and "Tests".
> 
> New under "Analysis": there's a "Bootstrap..." item.  This opens a 
> dialog box where you get to make five choices:
> 
> (1) The variable/coefficient to examine.
> 
> (2) "Confidence interval" vs "Studentized confidence interval" vs
>      "P-value".
> 
> (3) "Resampled residuals" vs "Simulate normal errors".
> 
> (4) Number of replications (default 1000).
> 
> (5) Show graph of bootstrap sampling distribution (no/yes).
> 
> Notes:
> 
> In relation to (1): you only get to examine one coefficient at a 
> time by this particular means.
> 
> On (2): the default (95%) confidence interval is based directly on 
> the quantiles of the bootstrap coefficient estimates.  The 
> "studentized" version is as per Davidson and MacKinnon's 
> "Econometric Theory and Methods" (ETM), chapter 5: at each bootstrap
> replication a t-ratio is formed as (a) the difference between the 
> current and the baseline coefficient estimate, divided by (b) the 
> baseline estimated standard error.  Then the confidence interval is 
> formed based on the quantiles of this t-ratio, as explained in ETM. 
> The "P-value" variant is, again, as explained in ETM.
> 
> On (3): you get to choose between resampling with replacement of the
> original residuals (rescaled as suggested in ETM), and simulated 
> normal errors with the empirically given variance. Andreas suggested
> including the option of "case resampling" (that is, resampling the 
> (y, X) pairs rather than the residuals.  I have not implemented this
> to date for two reasons: first, it seems statistically dodgy, and 
> second it is considerably more burdensome from the computational 
> viewpoint. (You can economize substantially if the X matrix is 
> treated as constant across the bootstrap replications.)
> 
> Point (4) should be mostly self-explanatory.  However, when you're 
> doing a (1 - alpha) confidence interval, then, as explained in ETM, 
> it is desirable that alpha(B + 1)/2 is an integer (where B is the 
> number of replications).  So gretl adjusts the user-chosen B value 
> to ensure this is the case.
> 
> Point (5) again should be self-explanatory: you can get gretl to 
> make a graph of the density of the bootstrapped coefficient or t-
> ratio. This option employs gretl's kernel density estimation facility.
> 
> The above all pertains to the "Analysis/Bootstrap" menu item.  In 
> addition you have options under "Tests/Linear restrictions".  The 
> restrictions dialog now has a "Use bootstrap" check box.  If you 
> check this, you get a bootstrapped F-test for whatever set of linear
> restictions you have entered.  The methodology is as described in 
> ETM for bootstrapped P-values.
> 
> Autoregressive models: If the set of regressors includes the first 
> lag of the dependent variable this should be handled correctly: the 
> bootstrap data sets are calculated recursively, taking into account 
> the autoregression.  Please note that higher-order autoregressions 
> are _not_ currently recognized and handled appropriately.
> 
> In script mode: For single-equation models estimated via OLS, you 
> can append the --boot flag to the "restrict" command to get 
> bootstrapped tests.  You can also set the default number of 
> bootstrap replications using the "set" command with "bootrep" 
> parameter.  For example:
> 
>   set bootrep 10000
> 
> Testing and comments welcome!
> 
> Allin.
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