Lavergne, Pascal and Vuong, Quang H. (1998) An integral estimator of residual variance and a measure of explanatory power of covariates in nonparametric regression. Journal of Nonparametric Statistics, 9 (4). pp. 363-380.

Abstract

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.