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gausscov (version 0.0.4)

The Gaussian Covariate Method for Variable Selection

Description

Given the standard linear model the traditional way of deciding whether to include the jth covariate is to apply the F-test to decide whether the corresponding beta coefficient is zero. The Gaussian covariate method is completely different. The question as to whether the beta coefficient is or is not zero is replaced by the question as to whether the covariate is better or worse than i.i.d. Gaussian noise. The P-value for the covariate is the probability that Gaussian noise is better. Surprisingly this can be given exactly and it is the same a the P-value for the classical model based on the F-distribution. The Gaussian covariate P-value is model free, it is the same for any data set. Using the idea it is possible to do covariate selection for a small number of covariates 25 by considering all subsets. Post selection inference causes no problems as the P-values hold whatever the data. The idea extends to stepwise regression again with exact probabilities. In the simplest version the only parameter is a specified cut-off P-value which can be interpreted as the probability of a false positive being included in the final selection. For more information see the website below and the accompanying papers: L. Davies and L. Duembgen, "Covariate Selection Based on a Model-free Approach to Linear Regression with Exact Probabilities", 2020, . L. Davies, "Lasso, Knockoff and Gaussian covariates: A comparison", 2018, .

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Version

Install

install.packages('gausscov')

Monthly Downloads

579

Version

0.0.4

License

GPL-3

Maintainer

Laurie Davies

Last Published

August 1st, 2020

Functions in gausscov (0.0.4)

ly.original

Leukemia data
frobregp

Robust regression using Huber's psi-function providing P-values
snspt

Sunspot data
frobreg

Robust regression using Huber's psi-function
fpval

Calculates the regression coefficients, the P-values and the standard P-values for the chosen subset ind
frmch

Robust selection of covariates based on all subsets
redwine

Redwine data
fsimords

Simulates the number of false positives for given dimensions (n,k) and given order statistics nu
decomp

decompose a given interaction ic into its component parts
lx.original

Leukemia data
mel-temp

Melbourne minimum temperature
frst

Robust stepwise selection of covariates
fselect

Selects the subsets specified by fmch.
fgr2st

Calculates an independence graph using repeated stepwise selection
fmch

Calculates all subsets where each included covariate is significant.
abcq

American Business Cycle
fgeninter

generation of interactions
decode

Decodes the number of a subset selected by flmmdch to give the covariates
fgentrig

generation of sine and cosine functions
f2st

Repeated stepwise selection of covariates
boston

Boston data
dent

Dental data
f1st

Stepwise selection of covariates
fgr1st

Calculates an independence graph using stepwise selection