Variance Function Estimation

Local Polynomial Variance Function Estimation

The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focussed on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The eeect of preliminary estimation of the mean is studied, and a \degrees of freedom"...

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...

Nonparametric variance function estimation with missing data

In this paper a fixed design regression model where the errors follow a strictly stationary process is considered. In this model the conditional mean function and the conditional variance function are unknown curves. Correlated errors when observations are missing in the response variable are assumed. Four nonparametric estimators of the conditional variance function based on local polynomial f...

Variance Function Estimation in High-dimensions

We consider the high-dimensional heteroscedastic regression model, where the mean and the log variance are modeled as a linear combination of input variables. Existing literature on high-dimensional linear regression models has largely ignored nonconstant error variances, even though they commonly occur in a variety of applications ranging from biostatistics to finance. In this paper we study a...

Variance Function Estimation in Heteroscedastic Regression Models