1995/06/01 by Hans‐Georg Müller, Peng-Liang Zhao · 2 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Econometrics #Heteroscedasticity #Mathematics #Nonparametric regression #Nonparametric statistics #Optimal Experimental Design Methods #Parametric statistics #Probabilistic and Robust Engineering Design #Regression analysis #Semiparametric model #Semiparametric regression #Statistics #Variance function
paper · pdf · doi:10.1214/aos/1176324630
openalex publication_date 1995/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
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 relation between the variance and the mean regression function is assumed to follow a generalized linear model. Almost all variance function models that were considered in the literature emerge as special cases. Least-squares-types estimates for the parameters of this model and the simultaneous estimation of the unknown regression and variance functions by means of nonparametric kernel estimates are combined to infer the parametric and nonparametric components of the proposed model. The asymptotic distribution of the parameter estimates is derived and is shown to follow usual parametric rates in spite of the presence of the nonparametric 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.