Asymptotic confidence interval for R² in multiple linear regression.

Dedecker, J.; Guedj, O.; Taupin, M. L.

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 $ R 2 under minimal moment conditions. We also give the asymptotic joint distribution of the empirical estimators of the individual $ R^2 $ R 2 '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 $ R 2 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.

ASYMPTOTIC distribution; STATISTICAL correlation; COVARIANCE matrices; CONFIDENCE intervals; HETEROSCEDASTICITY

Statistics, 2025, Vol 59, Issue 1, p1

0233-1888

Academic Journal

10.1080/02331888.2024.2428978