Abstract
This paper develops a bias correction scheme for a multivariate heteroskedastic errors-in-variables model. The applicability of this model is justified in areas such as astrophysics, epidemiology and analytical chemistry, where the variables are subject to measurement errors and the variances vary with the observations. We conduct Monte Carlo simulations to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates. We also give an application to a real data set.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akritas MG, Bershady MA (1996) Linear regression for astronomical data with measurement errors and intrinsic scatter. Astrophys J 470: 706–714
Cook RD, Tsai C, Wei B (1986) Bias in nonlinear regression. Biometrika 73: 615–623
Cordeiro GM (1993) Bartlett corrections and bias correction for two heteroskedastic regression models. Commun Stat Theory Methods 22: 169–188
Cordeiro GM (2008) Corrected maximum likelihood estimators in linear heteroskedastic regression models. Braz Rev Econom 28: 53–67
Cordeiro GM, Vasconcellos KLP (1997) Bias correction for a class of multivariate nonlinear regression models. Stat Probab Lett 35: 155–164
Cox DR, Hinkley DV (1974) Theoretical statistics. Chapman & Hall, London
de Castro M, Galea M, Bolfarine H (2008) Hypothesis testing in an errors-in-variables model with heteroskedastic measurement errors. Stat Med 27: 5217–5234
Doornik JA (2006) An object-oriented matrix language—Ox 4. Timberlake, 5th edn. Consultants Press, London
Fuller W (1987) Measurement error models. Wiley, Chichester
Kulathinal SB, Kuulasmaa K, Gasbarra D (2002) Estimation of an errors-in-variables regression model when the variances of the measurement error vary between the observations. Stat Med 21: 1089–1101
Patriota AG, Bolfarine H, de Castro M (2009) A heteroscedastic structural errors-in-variables model with equation error. Stat Methodol. doi:10.1016/j.stamet.2009.02.003
Patriota AG, Lemonte AJ (2009) Bias correction in a multivariate normal regression model with general parameterization. Stat Probab Lett. doi:10.1016/j.spl.2009.04.018
DevelopmentCore Team R. (2008) R: a language and environment for statistical computing. Austria, Vienna
Vasconcellos KLP, Cordeiro GM (1997) Approximate bias for multivariate nonlinear heteroskedastic regressions. Braz J Probab Stat 11: 141–159
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Patriota, A.G., Lemonte, A.J. & Bolfarine, H. Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model. Stat Papers 52, 455–467 (2011). https://doi.org/10.1007/s00362-009-0243-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-009-0243-7