Heteroscedastic additive models-estimating the fixed effects and covariance matrix parameters

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Abstract

This work aims to deduce estimators for the unknown parameters of fixed effects and covariance matrix structure in heteroscedastic additive design. In order to do that, the design will be projected onto the orthogonal complement of the subspace spanned by columns of design matrix for the fixed effects, and the Kronecker product will be used to produced unbiased estimators for the parameters of covariance matrix, and then such estimators used to produce an estimator for the fixed effect vector. Moreover, the coeffi-cient of determination for both fixed effects and covariance structure will be derived. A simulation study will be conducted, and a numerical example will be explored.

Original languageEnglish
Pages (from-to)579-593
Number of pages15
JournalHacettepe Journal of Mathematics and Statistics
Volume50
Issue number2
DOIs
Publication statusPublished - 2021

Keywords

  • Additive design
  • Heteroscedasticity
  • Kronecker product
  • Orthogonal matrix

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