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

Adilson Silva; Miguel Fonseca

doi:10.15672/hujms.647481

Araştırma Makalesi

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

Yıl 2021, , 579 - 593, 11.04.2021

Adilson Silva , Miguel Fonseca

https://doi.org/10.15672/hujms.647481

Öz

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.

Anahtar Kelimeler

orthogonal matrix, Kronecker product, additive design, heteroscedasticity

Destekleyen Kurum

New University of Lisbon

Proje Numarası

PEst-OE/MAT/UI0297/2011

Teşekkür

To Prof. Dr. João T. Mexia for the guidance.

Kaynakça

[1] A.C. Atkinson and R.D. Cook, D-optimum designs for heteroscedastic linear models, Amer.Statist. Assoc. 90 (429), 204-212, 1995.
[2] G.E. Battese and B.P. Bonyhady, Estimation of household expenditure functions: An application of a class of heteroscedastic regression models, Economic Record 57 (1), 1-22, 1981.
[3] C. Brenton, Linear Models. The Theory and Application of Analysis of Variance, John Wiley & Sons, Inc., 2008.
[4] M. Carapeto and W. Holt, Testing for heteroscedasticity in regression models, J. Appl. Stat. 30 (1), 13-20, 2003.
[5] K.S. Gordon, An efficient algorithm for REML in heteroscedastic regression, J. Comput. Graph. Statist. 11 (4), 836-847, 2002.
[6] A.C. Harvey, Estimating regression models with multiplicative heteroscedasticity, Econometrica 44 (3), 461-465, 1976.
[7] S.D. Horn, R.A. Horn and D.B. Duncan, Estimating heteroscedastic variances in linear models, J. Amer. Statist. Assoc. 70 (350), 380-385, 1975.
[8] D.J. Nott, M. Tran and C. Leng, Variational approximation for heteroscedastic linear models and matching pursuit algorithms, Stat. Comput. 22 (2), 497-512, 2012.
[9] J. Schott, Matrix Analysis for Statistics, John Wiley & Sons, Inc., 1997.
[10] A. Silva, Variance Components Estimation in Mixed Linear Models, Ph.D Thesis, New University of Lisbon, 2017.
[11] A.H. Welsh, R.J. Carroll and D. Ruppert, Fitting heteroscedastic regression models, J. Amer. Statist. Assoc. 89 (425), 100-116, 1994.

Yıl 2021, , 579 - 593, 11.04.2021

Adilson Silva , Miguel Fonseca

https://doi.org/10.15672/hujms.647481

Öz

Proje Numarası

PEst-OE/MAT/UI0297/2011

Kaynakça

[1] A.C. Atkinson and R.D. Cook, D-optimum designs for heteroscedastic linear models, Amer.Statist. Assoc. 90 (429), 204-212, 1995.
[2] G.E. Battese and B.P. Bonyhady, Estimation of household expenditure functions: An application of a class of heteroscedastic regression models, Economic Record 57 (1), 1-22, 1981.
[3] C. Brenton, Linear Models. The Theory and Application of Analysis of Variance, John Wiley & Sons, Inc., 2008.
[4] M. Carapeto and W. Holt, Testing for heteroscedasticity in regression models, J. Appl. Stat. 30 (1), 13-20, 2003.
[5] K.S. Gordon, An efficient algorithm for REML in heteroscedastic regression, J. Comput. Graph. Statist. 11 (4), 836-847, 2002.
[6] A.C. Harvey, Estimating regression models with multiplicative heteroscedasticity, Econometrica 44 (3), 461-465, 1976.
[7] S.D. Horn, R.A. Horn and D.B. Duncan, Estimating heteroscedastic variances in linear models, J. Amer. Statist. Assoc. 70 (350), 380-385, 1975.
[8] D.J. Nott, M. Tran and C. Leng, Variational approximation for heteroscedastic linear models and matching pursuit algorithms, Stat. Comput. 22 (2), 497-512, 2012.
[9] J. Schott, Matrix Analysis for Statistics, John Wiley & Sons, Inc., 1997.
[10] A. Silva, Variance Components Estimation in Mixed Linear Models, Ph.D Thesis, New University of Lisbon, 2017.
[11] A.H. Welsh, R.J. Carroll and D. Ruppert, Fitting heteroscedastic regression models, J. Amer. Statist. Assoc. 89 (425), 100-116, 1994.

Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	İstatistik
Bölüm	İstatistik
Yazarlar	Adilson Silva 0000-0003-1786-1192 Miguel Fonseca 0000-0002-0162-8372
Proje Numarası	PEst-OE/MAT/UI0297/2011
Yayımlanma Tarihi	11 Nisan 2021
Yayımlandığı Sayı	Yıl 2021

Kaynak Göster

APA	Silva, A., & Fonseca, M. (2021). Heteroscedastic additive models - Estimating the fixed effects and covariance matrix parameters. Hacettepe Journal of Mathematics and Statistics, 50(2), 579-593. https://doi.org/10.15672/hujms.647481
AMA	Silva A, Fonseca M. Heteroscedastic additive models - Estimating the fixed effects and covariance matrix parameters. Hacettepe Journal of Mathematics and Statistics. Nisan 2021;50(2):579-593. doi:10.15672/hujms.647481
Chicago	Silva, Adilson, ve Miguel Fonseca. “Heteroscedastic Additive Models - Estimating the Fixed Effects and Covariance Matrix Parameters”. Hacettepe Journal of Mathematics and Statistics 50, sy. 2 (Nisan 2021): 579-93. https://doi.org/10.15672/hujms.647481.
EndNote	Silva A, Fonseca M (01 Nisan 2021) Heteroscedastic additive models - Estimating the fixed effects and covariance matrix parameters. Hacettepe Journal of Mathematics and Statistics 50 2 579–593.
IEEE	A. Silva ve M. Fonseca, “Heteroscedastic additive models - Estimating the fixed effects and covariance matrix parameters”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, ss. 579–593, 2021, doi: 10.15672/hujms.647481.
ISNAD	Silva, Adilson - Fonseca, Miguel. “Heteroscedastic Additive Models - Estimating the Fixed Effects and Covariance Matrix Parameters”. Hacettepe Journal of Mathematics and Statistics 50/2 (Nisan 2021), 579-593. https://doi.org/10.15672/hujms.647481.
JAMA	Silva A, Fonseca M. Heteroscedastic additive models - Estimating the fixed effects and covariance matrix parameters. Hacettepe Journal of Mathematics and Statistics. 2021;50:579–593.
MLA	Silva, Adilson ve Miguel Fonseca. “Heteroscedastic Additive Models - Estimating the Fixed Effects and Covariance Matrix Parameters”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 2, 2021, ss. 579-93, doi:10.15672/hujms.647481.
Vancouver	Silva A, Fonseca M. Heteroscedastic additive models - Estimating the fixed effects and covariance matrix parameters. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):579-93.