Title: Combined permutation tests for linear regression models
Authors: Stefano Bonnini - University of Ferrara (Italy) [presenting]
Abstract: In the econometric literature, several contributions have been dedicated to permutation solutions for linear model selection. A permutation version of the ANOVA test for a linear regression model with $q$ explanatory variables might be based on the $F$ test statistic. Its null permutation distribution might be obtained by permuting the vector of observed values of the dependent variable and keeping the columns of regressors fixed. As alternative, we propose a solution based on the combination of the partial permutation tests on the single regression coefficients. This method has the advantage that the overall test on the full model is broken down into $q$ sub-problems and may be intended as a multiple test. By means of a suitable correction of the partial $p$-values, it allows the detection of the relevant predictive variables avoiding the inflation of the type I error rate of the overall test. Thus it is a nonparametric alternative to the backward elimination method or other stepwise procedures, with two main advantages: it is time saving and it controls the type I error probability. Good power behaviour and utility of the method are shown through simulations and application to a real problem.