Likelihood and parametric heteroscedasticity in normal connected linear models

Joao Tiago Mexia; Pedro Corte Real

Discussiones Mathematicae Probability and Statistics (2000)

  • Volume: 20, Issue: 2, page 177-188
  • ISSN: 1509-9423

Abstract

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A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.

How to cite

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Joao Tiago Mexia, and Pedro Corte Real. "Likelihood and parametric heteroscedasticity in normal connected linear models." Discussiones Mathematicae Probability and Statistics 20.2 (2000): 177-188. <http://eudml.org/doc/287719>.

@article{JoaoTiagoMexia2000,
abstract = {A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.},
author = {Joao Tiago Mexia, Pedro Corte Real},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {linear model; connected model; normal model; maximum likelihood estimators; score function; Newton-Raphson method; connected models},
language = {eng},
number = {2},
pages = {177-188},
title = {Likelihood and parametric heteroscedasticity in normal connected linear models},
url = {http://eudml.org/doc/287719},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Joao Tiago Mexia
AU - Pedro Corte Real
TI - Likelihood and parametric heteroscedasticity in normal connected linear models
JO - Discussiones Mathematicae Probability and Statistics
PY - 2000
VL - 20
IS - 2
SP - 177
EP - 188
AB - A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.
LA - eng
KW - linear model; connected model; normal model; maximum likelihood estimators; score function; Newton-Raphson method; connected models
UR - http://eudml.org/doc/287719
ER -

References

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  3. [3] W.C. Davidson, Variable Metric Methods for Minimization, Atomic Energy Commision, Research Development Report ANL-5990, Washington, D.C. 1959. 
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  7. [7] J.D. Jobson and W.A. Fuller, Least Squares Estimation When the Covariance Matrix and Parameter Vector Are Functionally Related, Journal of the American Statistical Association 75 (1980), 176-181. Zbl0437.62064
  8. [8] J.L. Kelley, General Topology, Princeton, New Jersey 1961. Zbl0157.53002
  9. [9] J.T. Mexia, Linear Models with Partially Controlled Heteroscedasticity, Trabalhos de Investigaçao 2. Departamento de Matemática - Faculdade de Ciencias e Tecnologia/Universidade Nova de Lisboa 1993. Zbl0806.62054
  10. [10] R.L. Plackett, Principles of Regression Analysis, Oxford University Press, Oxford 1960. Zbl0091.31301
  11. [11] S.J. Prais and H.S. Houthakker, The Analysis of Family Budgets, Cambridge University Press, Cambridge 1955. 
  12. [12] C.R. Rao, Linear Statistical Inference and Its Applications (Second Edition), John Wiley & Sons 1973. Zbl0256.62002

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