Nonparametric multiplicative heteroscedasticity in multi-dimensional regression

In many statistical applications, the variability of the data is an important issue. For instance, in the regression analysis, researchers often meet the heteroscedasticity problem. There is a wide body of literature about the nonparametric estimation of the conditional variance function in one-dimensional case. However there are only few papers about the nonparametric estimation of the conditional variance function when there are several regressors in the model. In this paper, we propose a smooth backfitting estimator for the multiplicative conditional variance function and study the asymptotic property and finite sample performance via simulation studies.