Some shrunken predictors in finite populations with a multinormal superpopulation model

In this paper 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.