Variance function partially linear single‐index models Academic Article uri icon

abstract

  • We consider heteroscedastic regression models where the mean function is a partially linear single index model and the variance function depends upon a generalized partially linear single index model. We do not insist that the variance function depend only upon the mean function, as happens in the classical generalized partially linear single index model. We develop efficient and practical estimation methods for the variance function and for the mean function. Asymptotic theory for the parametric and nonparametric parts of the model is developed. Simulations illustrate the results. An empirical example involving ozone levels is used to further illustrate the results, and is shown to be a case where the variance function does not depend upon the mean function.

author list (cited authors)

  • Lian, H., Liang, H., & Carroll, R. J.

citation count

  • 19

publication date

  • April 2014

publisher