ON A SEMIPARAMETRIC VARIANCE FUNCTION MODEL AND A TEST FOR HETEROSCEDASTICITY

We propose a general semiparametric variance function model in a fixed design regression setting. In this model, the regression function is assumed to be smooth and is modelled nonparametrically, whereas the re lation between the variance and the mean regression function is assume d to follow a generalized linear model. Almost all variance function m odels that were considered in the literature emerge as special cases. Least-squares-type estimates for the parameters of this model and the simultaneous estimation of the unknown regression and variance functio ns by means of nonparametric kernel estimates are combined to infer th e parametric and nonparametric components of the proposed model. The a symptotic distribution of the parameter estimates is derived and is sh own to follow usual parametric rates in spite of the presence of the n onparametric component in the model. This result is applied to obtain a data-based test for heteroscedasticity under minimal assumptions on the shape of the regression function.