Testing Hypotheses in High Dimensional Regression

Abstract

In this paper, we test the hypotheses concerning the regression coefficients once by using the lasso model, then by using islasso model (proposed by Giovanna et al, 2019), where the islasso model is considered to be an alternative procedure for the regression splines model, where the bandwidth is determined by the corresponding standard error calculated by the data and allows the covariance matrix and Wald statistic to be obtained relatively easily.The results of the simulation showed better importance for the islasso regression model in the case of small and medium samples (n <50). also, it was found when the sample size increases and the standard error decreases, the islasso gets closer to the original lasso, making the islasso asymptotically equivalent to the lasso.