TY  - JOUR
T1  - Heteroscedastic additive models - Estimating the fixed effects and covariance matrix parameters
AU  - Silva, Adilson
AU  - Fonseca, Miguel
PY  - 2021
DA  - April
DO  - 10.15672/hujms.647481
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 579
EP  - 593
VL  - 50
IS  - 2
LA  - en
AB  - 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 coefficient 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.
KW  - orthogonal matrix
KW  - Kronecker product
KW  - additive design
KW  - heteroscedasticity
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UR  - https://doi.org/10.15672/hujms.647481
L1  - https://dergipark.org.tr/en/download/article-file/856234
ER  -