J. U. Breckling, R. L. Chambers, A. H. Dorfman, S. M. Tam, A. H. Welsh, Maximum Likelihood Inference from Sample Survey Data, International Statistical Review / Revue Internationale de Statistique, Vol. 62, No. 3 (Dec., 1994), pp. 349-363
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Breckling et al. (1994) studied this question.
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