Asymptotic confidence interval for R2 in multiple linear regression

Following White's approach of robust multiple linear regression [White H. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 1980;48(4):817-838], we give asymptotic confidence intervals for the multiple correlation coefficient $ R<^>2 $ R2 under minimal moment conditions. We also give the asymptotic joint distribution of the empirical estimators of the individual $ R<^>2 $ R2's. Through different sets of simulations, we show that the procedure is indeed robust (contrary to the procedure involving the near exact distribution of the empirical estimator of $ R<^>2 $ R2 is the multivariate Gaussian case) and can be also applied to count linear regression. Several extensions are also discussed, as well as an application to robust screening.