Some shrunken predictors in finite populations with a multinormal superpopulation model (Q1094020)

We derive some alternative estimators of the superparameter and predictors of the population total for a multinormal superpopulation model. The estimators and predictors obtained are better than the maximum likelihood predictor near the ``natural origin'' though possibly worse farther away. The technique employed is to shrink the maximum likelihood predictor towards a ``natural origin''. With a numerical example, it is shown that the shrunken predictor of the population total works better than the maximum likelihood predictor for small sample sizes and near the ``natural origin''. A combined predictor which is not as good as the shrunken predictor near the origin but not disasterously far away from the origin is introduced.