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covariance
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Covariance Statistic and a Significance Test for Selecting All Active Variables
in Lasso
,
M.Sc. Thesis
Sharif University of Technology
;
Abstract
Testing the significance of the predictor variables and finding an appropriate method for inference on the coefficients is an important question in the sparse linear regression setting. Covariance statistic is a new method that tries to give an answer to this question. This statistic is defined based on lasso fitted values, and when the true model is linear, this statistic has an Exp(1) asymptotic distribution under the null hypothesis (the null being that all truly active variables are contained in the current lasso model). From classical statistics, we have known some methods like chi-squared test for testing the significance of an additional variable between two nested linear models. But...