The use of mixtures for dealing with non-normal regression errors

In many situations, the distribution of the error terms of a linear regression model departs significantly from normality. It is shown, through a simulation study, that an effective strategy to deal with these situations is fitting a regression model based on the assumption that the error terms follow a mixture of normal distributions. The main advantage, with respect to the usual approach based on the least-squares method is a greater precision of the parameter estimates and confidence intervals. For the parameter estimation we make use of the EM algorithm, while confidence intervals are constructed through a bootstrap method.

[1]  J. B. Ramsey,et al.  Estimating Mixtures of Normal Distributions and Switching Regressions , 1978 .

[2]  H. L. Le Roy,et al.  Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; Vol. IV , 1969 .

[3]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[4]  M. Aitkin,et al.  Mixture Models, Outliers, and the EM Algorithm , 1980 .

[5]  B. Bolch,et al.  On the Testing of Regression Disturbances for Normality , 1974 .

[6]  Jeff A. Bilmes,et al.  A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models , 1998 .

[7]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[8]  M. Wand,et al.  EXACT MEAN INTEGRATED SQUARED ERROR , 1992 .

[9]  M. Kenward,et al.  An Introduction to the Bootstrap , 2007 .

[10]  K. Koehler,et al.  Probability Plots and Distribution Curves for Assessing the Fit of Probability Models , 1991 .

[11]  Gunnar Blom,et al.  Statistical Estimates and Transformed Beta-Variables. , 1960 .

[12]  David R. Cox,et al.  A Note on the Efficiency of Least-squares Estimates , 1968 .

[13]  K. Koehler,et al.  Goodness-of-fit tests based on P—P probability plots , 1990 .

[14]  F. J. Anscombe,et al.  Examination of Residuals , 1961 .

[15]  F. David,et al.  Statistical Estimates and Transformed Beta-Variables. , 1960 .

[16]  S. Looney,et al.  Use of the Correlation Coefficient with Normal Probability Plots , 1985 .