# gausscov v0.0.4

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## The Gaussian Covariate Method for Variable Selection

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, <arXiv:1906.01990>. L. Davies, "Lasso, Knockoff and Gaussian covariates: A comparison", 2018, <arXiv:1807.09633>.

## Functions in gausscov

 Name Description 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 No Results!