Induced smoothing in LASSO regression

The thesis is being carried out with the National research Council at the Institute of Biomedicine and Molecular Immunology "Alberto Monroy" of Palermo, where I am a fellow, under the supervision of MD Stefania La Grutta. Our research unit is focused on clinical research in allergic respiratory problems in children. In particular, we are interested in to assess the determinants of impaired lung function in a sample of outpatient asthmatic children aged between 5 and 17 years enrolled from 2011 to 2017. Our dataset is composed by n = 529 children and several covariates regarding host and environmental factors. This thesis focuses on hypothesis testing in lasso regression, when one is interested in judging statistical significance for the parameters involved in the regression equation. To get reliable p-values we propose a new lasso-type estimator relying on the recent idea of induced smoothing which allows to obtain appropriate covariance matrix and Wald statistic relatively easily. In addition, we discuss the score statistic to carry out interval estimation on the regression coefficients in LASSO regression. Some simulation experiments reveal our approaches exhibits better performance when contrasted with the recent inferential tools in the lasso framework. Finally, we analysed data regarding asthmatic out-patient children which motivated our project.