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ROBUST MODELLING IN MEASUREMENT ERROR MODELS USING THE t DISTRIBUTION
Heleno Bolferine and Reinaldo B. Arellano-Valle
Brazilian Journal of Probability and Statistics
Vol. 8, No. 1, SPECIAL ISSUE: V CLAPEM PROCEEDINGS (MAY 1994), pp. 67-84
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/43600850
Page Count: 18
You can always find the topics here!Topics: Maximum likelihood estimators, T distribution, Parametric models, Estimators, Datasets, Maximum likelihood estimation, Regression analysis, Degrees of freedom, Statistical estimation, Least squares
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Most of the literature in measurement error models deals with normally distributed errors. In this paper, a robust extension of normal measurement error models is considered by using the t-family of distributions to model the kurtoeis of the error distributions. The analytical approach is based on maximum likelihood and applications are considered for both, the functional and structural regression models. As it happens with ordinary regression models, the degrees of freedom parameter of the t distribution provides a convenient and practical way of achieving robust inference in measurement error models with slight increase in computational complexity. In both cases, the degrees of freedom parameter is orthogonal to the regression parameters in the sense of Cox and Reid (1987), which means that there is no increase in the asymptotic variance of the quantities of interest due to the estimation of the extra parameter. Applications to real data sets are also reported.
Brazilian Journal of Probability and Statistics © 1994 Brazilian Statistical Association