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 l} under general conditions and derive a nonparametric decomposition of the variance formula. Monte-Carlo experiments suggest that the estimator has good small sample properties.

Keywords:

• Residual variance
• nonparametric R-squared