Variance function partially linear single-index models

Publication Type:
Journal Article
Journal of the Royal Statistical Society. Series B: Statistical Methodology, 2015, 77 (1), pp. 171 - 194
Issue Date:
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© 2014 Royal Statistical Society. We consider heteroscedastic regression models where the mean function is a partially linear single-index model and the variance function depends on a generalized partially linear single-index model. We do not insist that the variance function depends only on 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 non-parametric parts of the model is developed. Simulations illustrate the results. An empirical example involving ozone levels is used to illustrate the results further and is shown to be a case where the variance function does not depend on the mean function.
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