Adaptive variance function estimation in heteroscedastic nonparametric regression

Adaptive Variance Function Estimation in Heteroscedastic Nonparametric Regression

We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences of the observations. We show that the variance function estimator is nearly optimally adaptive to the smoothness of both the mean and variance functions. Th...

Variance Function Estimation in Heteroscedastic Regression Models

Optimal Difference-based Variance Estimation in Heteroscedastic Nonparametric Regression

Estimating the residual variance is an important question in nonparametric regression. Among the existing estimators, the optimal difference-based variance estimation proposed in Hall, Kay, and Titterington (1990) is widely used in practice. Their method is restricted to the situation when the errors are independent and identically distributed. In this paper, we propose the optimal difference-b...

Variance Function Estimation in Multivariate Nonparametric Regression

Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established. Our work uses the approach that generalizes the one used in Munk et al (2005) for the constant variance case. As is the case when the number of dimensions d = 1, and very much contrary to the common practice, it is often not desirable to base the estimator of t...

Variance function estimation in multivariate nonparametric regression with fixed design

Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established in the iid Gaussian case. Our work uses the approach that generalizes the one used in [A. Munk, Bissantz, T. Wagner, G. Freitag, On difference based variance estimation in nonparametric regression when the covariate is high dimensional, J. R. Stat. Soc. B 67 (Pa...