If an example of a linear model you are referring to is running a linear
regression. Here some thoughts.
You cannot simulate all distributions when testing for coefficients in a
linear regressions without making
any assumptions on the error distributions. The space of all
distributions is infinitely dimensional.
This cannot be simulated.
There is no need run simulations, just use an exact method. These do not
require simulations as their type I
error is controlled. For linear regressions with mean of errors = 0 you
can use Gossner and Schlag (2012).
If instead you wish to assume that errors have median = 0 choose one of
the many papers of Dufour and coauthors
eg Dufour and Taamouti (2010).
Greetings, Karl (I will be happy to explain off the list more about the
details to anyone interested)
Dufour, J.-M., and A. Taamouti (2010): Exact optimal inference in regression
models under heteroskedasticity and non-normality of unknown form,"
Statistics and Data Analysis, 54, 2532-2553.
Gossner and Schlag (2012):
software at: http://homepage.univie.ac.at/karl.schlag/ under "Research"
On 16.03.2012 01:39, Vincent Granville wrote:
> Interesting follow-up to the question "Has a degree in mathematics become worthless?" posted on Analyticbridge at
> http://www.analyticbridge.com/profiles/blogs/has-a-degree-in-mathematics-become-worthless-ieee :
> A related question: should general linear models (for statistical inference) still be taught? Shouldn't the curriculum focus on sophisticated computer-intensive simulations to conpute confidence intervals and for statistical analyses in general? The advantages are:
> - easy to code, no use of black box software anymore
> - data driven, model-free, non parametric approach, applies to any type of data
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