Search results for "sandwich formula"

Inferential tools in penalized logistic regression for small and sparse data: A comparative study.

2016

This paper focuses on inferential tools in the logistic regression model fitted by the Firth penalized likelihood. In this context, the Likelihood Ratio statistic is often reported to be the preferred choice as compared to the ‘traditional’ Wald statistic. In this work, we consider and discuss a wider range of test statistics, including the robust Wald, the Score, and the recently proposed Gradient statistic. We compare all these asymptotically equivalent statistics in terms of interval estimation and hypothesis testing via simulation experiments and analyses of two real datasets. We find out that the Likelihood Ratio statistic does not appear the best inferential device in the Firth penal…

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 interes…

Penalized logistic regression for small or sparse data: interval estimators revisited

2015

This paper focuses on interval estimation in logistic regression models fitted through the Firth penalized log-likelihood. In this context, many authors have claimed superiority of the Likelihood ratio statistic with respect to the (wrong) Wald statistic via simulation evidence. We re-assess such findings by detailing the inferential tools also including in the comparisons the (right) Wald statistic and other statistics neglected in previous literature. In particular, we assess performances of the CIs estimators by simulation and compare them in a real data set. Differently from previous findings, the Likelihood ratio statistic does not appear to be the best inferential device in Firth pena…

The Induced Smoothed lasso: A practical framework for hypothesis testing in high dimensional regression.

2020

This paper focuses on hypothesis testing in lasso regression, when one is interested in judging statistical significance for the regression coefficients in the regression equation involving a lot of covariates. To get reliable p-values, we propose a new lasso-type estimator relying on the idea of induced smoothing which allows to obtain appropriate covariance matrix and Wald statistic relatively easily. Some simulation experiments reveal that our approach exhibits good performance when contrasted with the recent inferential tools in the lasso framework. Two real data analyses are presented to illustrate the proposed framework in practice.