On Sat, Apr 18, 2015 at 9:45 PM, Sturla Molden <sturla.mol...@gmail.com> wrote:
> <josef.p...@gmail.com> wrote:
>
>> (I just went through some articles to see how we can produce p-values
>> after feature selection with penalized least squares or maximum
>> penalized likelihood. :)
>
> If you have used penalized least squares or penalized likelihood, you have
> already pruned the model for parameters that only contributes to
> overfitting. If the p-value subsequently informs you that a parameter in
> the model of maximum parsimony is "not significant", you have reached the
> absurd conclusion that a parameter which should be in the model has no
> effect.

(LASSO selects too many variables, according to what I just read. That
is, it also selects parameters that are zero.)

That's a good argument. So we better ignore our p-value column in the
standard results table.
Fan and Li use confidence interval coverage to check the accuracy of
the asymptotic distribution after feature selection.

However, we still have tests of other linear (and soon nonlinear)
restrictions on the parameters. Are these two parameters the same? Do
they add up to one? Is this parameter equal to pi? and so on.

And we might want to tests parameters that we don't penalize.

Josef


>
> Sturla
>
>
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