VARIANCE ESTIMATION IN NONPARAMETRIC MULTIPLE REGRESSION

ABSTRACT

We consider the variance estimation in a general nonparametric regression model with multiple covariates. We extend difference methods to the multivariate setting by introducing an algorithm that orders the design points in higher dimensions. We also consider an adaptive difference estimator which requires much less strict assumptions on the covariate design and can significantly reduce mean squared error for small sample sizes.

Keywords:

• Nonparametric regression surface
• Difference method
• Asymptotic distribution
• Sparse design

Acknowledgments