An integral estimator of residual variance and a measure of explanatory power of covariates in nonparametric regression

Résumé

We propose a new estimator of unconditional residual variance in nonparametric regression based on the integral of squared residuals. We show its consistency in L1 under general conditions and derive a nonparametric decomposition of the variance formula. Monte-Carlo experiments suggest that the estimator has good small sample properties.

Référence

Pascal Lavergne et Quang Vuong, « An integral estimator of residual variance and a measure of explanatory power of covariates in nonparametric regression », Journal of Nonparametric Statistics, vol. 9, n° 4, 1998, p. 363–380, 18 pages.