Effect Of Mean On Variance Function Estimation In Nonparametric Regression
Lie Wang, Lawrence Brown, Tony Cai, and Michael Levine
Variance function estimation in nonparametric regression is considered
and the minimax rate of convergence is derived. We are particularly
interested in the effect of the unknown mean on the estimation of the
variance function. Our results indicate that, contrary to the common
practice, it is often not
desirable to base the estimator of the variance function on the
residuals from an optimal estimator of the mean. Instead
it is desirable to use estimators of the mean with minimal bias.
In addition the results also correct the optimal rate claimed
in the previous literature.