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

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.

Reference

Pascal Lavergne, and 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, pp. 363–380, 18 pages.