A lack-of-fit test for heteroscedastic regression models via cosine-series smoothers

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Abstract

In this paper, a test is derived to assess the validity of heteroscedastic nonlinear regression models by a non-parametric cosine regression method. For order selection, the paper proposes a data-driven method that uses the parametric null model optimal order. This method yields a test that is asymptotically normally distributed under the null hypothesis and is consistent against any fixed alternative. Simulation studies that test the lack of fit of a generalized linear model are conducted to compare the performance of the proposed test with that of an existing non-parametric kernel test. A dataset of esterase levels is used to demonstrate the proposed method in practice.

Original languageEnglish (US)
Pages (from-to)477-489
Number of pages13
JournalAustralian and New Zealand Journal of Statistics
Volume45
Issue number4
StatePublished - Dec 2003
Externally publishedYes

Keywords

  • Cosine-series smoother
  • Fit-comparison test
  • Order selection
  • Quasi-likelihood estimator

ASJC Scopus subject areas

  • Statistics and Probability

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