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A Regression Technique Accounting for Heteroscedastic and Asymmetric Errors

Michael S. Williams
Journal of Agricultural, Biological, and Environmental Statistics
Vol. 2, No. 1 (Mar., 1997), pp. 108-129
Stable URL: http://www.jstor.org/stable/1400643
Page Count: 22
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A Regression Technique Accounting for Heteroscedastic and Asymmetric Errors
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Abstract

Regression models are often used for estimating net outputs of a biological system. In many cases both heteroscedasticity and asymmetry of the errors are encountered. Properly accounting for the effects of these types of errors can substantially improve the estimation of regression coefficients and prediction intervals. Transformations, such as those proposed by Box and Cox (1964), are used extensively to obtain homoscedasticity and symmetry of errors. One of the major drawbacks of transformation methods is that when both heteroscedasticity and asymmetry are present, a transformation that corrects for both may not exist. A regression method based on modeling the error distribution using Johnson's (1949) SU distribution is proposed and referred to as SU regression. This new regression technique is compared with the weighted and unweighted transformation of both sides methods using two forestry datasets. For both datasets the assumption of SU distributed errors was appropriate, but neither of the transformation of both sides methods was able to achieve symmetric residuals. Clear improvements in the prediction intervals for SU regression were demonstrated in a cross-validated simulation.

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