| Name : R-gausscov
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| Version : 1.1.3
| Vendor : obs://build_opensuse_org/devel:languages:R
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| Release : lp153.2.2
| Date : 2024-06-14 11:09:31
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| Group : Development/Libraries/Other
| Source RPM : R-gausscov-1.1.3-lp153.2.2.src.rpm
|
| Size : 1.89 MB
| |
| Packager : (none)
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| Summary : The Gaussian Covariate Method for Variable Selection
|
Description :
The standard linear regression theory whether frequentist or Bayesian
is based on an \'assumed (revealed?) truth\' (John Tukey) attitude to
models. This is reflected in the language of statistical inference
which involves a concept of truth, for example confidence intervals,
hypothesis testing and consistency. The motivation behind this package
was to remove the word true from the theory and practice of linear
regression and to replace it by approximation. The approximations
considered are the least squares approximations. An approximation is
called valid if it contains no irrelevant covariates. This is
operationalized using the concept of a Gaussian P-value which is the
probability that pure Gaussian noise is better in term of least squares
than the covariate. The precise definition given in the paper, it is
intuitive and requires only four simple equations. Its overwhelming
advantage compared with a standard F P-value is that is is exact and
valid whatever the data. In contrast F P-values are only valid for
specially designed simulations. Given this a valid approximation is one
where all the Gaussian P-values are less than a threshold p0 specified
by the statistician, in this package with the default value 0.01. This
approximations approach is not only much simpler it is overwhelmingly
better than the standard model based approach. The will be demonstrated
using six real data sets, four from high dimensional regression and two
from vector autoregression. The simplicity and superiority of Gaussian
P-values derive from their universal exactness and validity. This is in
complete contrast to standard F P-values which are valid only for
carefully designed simulations. The function f1st is the most important
function. It is a greedy forward selection procedure which results in
either just one or no approximations which may however not be valid. If
the size is less than than a threshold with default value 21 then an
all subset procedure is called which returns the best valid subset. A
good default start is f1st(y,x,kmn=15) The best function for returning
multiple approximations is f3st which repeatedly calls f1st. For more
information see the web site below and the accompanying papers: L.
Davies and L. Duembgen, \"Covariate Selection Based on a Model-free
Approach to Linear Regression with Exact Probabilities\", 2202,
< doi:10.48550/arXiv.2202.01553>. L. Davies, \"An Approximation Based
Theory of Linear Regression\", 2402, < doi:10.48550/arXiv.2402.09858>.
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