Variance function estimation via model selection

• Autorzy: Teresa Ledwina , Jan Mielniczuk
• Języki publikacji: EN

Abstrakty

EN

The problem of estimating an unknown variance function in a random design Gaussian heteroscedastic regression model is considered. Both the regression function and the logarithm of the variance function are modelled by piecewise polynomials. A finite collection of such parametric models based on a family of partitions of support of an explanatory variable is studied. Penalized model selection criteria as well as post-model-selection estimates are introduced based on Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML) methods of estimation of the parameters of the models. The estimators are defined as ML or REML estimators in the models with dimensions determined by respective selection rules. Some encouraging simulation results are presented and consistency results on the solution pertaining to ML estimation for this approach are proved.

Kategorie tematyczne

• 62G20: Asymptotic properties
• 62F12: Asymptotic properties of estimators
• 62J99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2010
• Tom: 37
• Numer: 4
• Strony: 387-411

Daty

wydano

2010

Twórcy

autor

Teresa Ledwina

• Institute of Mathematics, Polish Academy of Sciences, Kopernika 18, 51-617 Wrocław, Poland

autor

Jan Mielniczuk

• Institute of Computer Science, Ordona 21, 01-237 Warszawa, Poland
• Warsaw University of Technology, Plac Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/am37-4-1