How Can I Use PROC ENTROPY Properly to Yield BLUE Estimates?

[OneEyedKing]

I am seeking to use PROC ENTROPY to model a cost function, but I can see evidence of heteroskedasticity in the omnibus studentized residual plot that I hope to remediate. Ideally, I would like to conform to the usual "rules of road" in using the variance (i.e. squared residuals) but as I am not as familiar with PROC ENTROPY I don't want to blindly apply something from OLS that would not be appropriate under GME. For example, in reviewing the documentation for WEIGHT option in PROC ENTROPY:

The regressors and the dependent variables are multiplied by the square root of the weight variable to form the weighted matrix and the weighted dependent variable.

This differs from the implementation of the WEIGHT option in PROC GLM:

If the weights for the observations are proportional to the reciprocals of the error variances, then the weighted least squares estimates are best linear unbiased estimators (BLUE).

I do not understand why there are two different implementations of weighting between ENTROPY and GLM, thus this question.

Thanks for any insights you can offer me regarding this issue.

[sbxkoenk]

The ENTROPY procedure implements a parametric method of linear estimation based on generalized maximum entropy (GME).
The ENTROPY procedure is suitable when there are outliers in the data and robustness is required, when the model is ill-posed or under-determined for the observed data, or for regressions that involve small data sets.

Is your data ill-behaved? Do you have a small sample?

PROC ENTROPY estimates tend to be biased (slightly biased), as they are a type of shrinkage estimate, but typically portray smaller variances than ordinary least squares (OLS) counterparts, making them more desirable from a mean squared error (MSE) viewpoint.

[sbxkoenk]

If you are not dealing with ill-behaved data and/or with a small sample, there are many other ways (besides PROC ENTROPY) to deal with heteroskedasticity in regression residuals.

See here:

• 131-2007: Skewness, Multicollinearity, Heteroskedasticity – You Name It, Cost Data Have It! Solution...
  
  Skewness, Multicollinearity, Heteroskedasticity - You Name It, Cost Data Have It! Solutions to Violations of Assumptions of Ordinary Least Squares Regression Models Using SAS®
  Leonor Ayyangar -- Health Economics Resource Center (HERC)
  VA Palo Alto Health Care System Menlo Park, CA
  (a SAS Global Forum 2007 paper, but still valid info of course)
  
  
• 60848 - A Simple Regression Model with Correction of Heteroscedasticity  (application of SAS/ETS PROC MODEL)

Ciao,
Koen