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A general approach to heteroscedastic linear
regression
by David Leslie, Robert Kohn and David J. Nott
Our article presents a general treatment of the linear regression model,
in which the error distribution is modelled nonparametrically and the error
variances may be heteroscedastic, thus eliminating the need to transform
the dependent variable in many data sets. The mean and variance components of the model may be either parametric or nonparametric, with
parsimony achieved through variable selection and model averaging. A
Bayesian approach is used for inference with priors that are data-based
so that estimation can be carried out automatically with minimal input
by the user. A Dirichlet process mixture prior is used to model the error
distribution nonparametrically; when there are no regressors in the model,
the method reduces to Bayesian density estimation, and we show that in
this case the estimator compares favourably with a well-regarded plug-in
density estimator. We also consider a method for checking the fit of the
full model. The methodology is applied to a number of simulated and real
examples and is shown to work well.
Key words: density estimation; Dirichlet process mixture; heteroscedasticity; model checking; nonparametric regression; variable selection.
Full text of the paper (pdf),
to appear in Statistics and Computing.
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