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With proper unit-weighting, the widely used statistical packages provide unbiased estimates of means, proportions, and totals for disproportionately stratified samples but generally overestimate these statistics' variances. Proper unit-weighting need not artificially increase the sample size. If the assumptions of classical linear regression are appropriate and the model is correctly specified, then ordinary least-squares regression without unit-weighting provides the best-linear-unbiased and maximum-likelihood estimates for large stratified samples-at least for those with small sampling proportions from large populations. With heteroscedastic errors, generalized least-squares can be performed through data transformations.
Kent W. Smith (Mon,) studied this question.