** by Forough
Karlberg**

** Research
Report 1997:1**

Department of Statistics, Stockholm University, S-106 91 Stockholm, Sweden

**Abstract**

The population total for a highly skewed finite population is studied, in the presence of auxiliary variables. A multivariate lognormal superpopulation model is assumed, the model parameters are ML-estimated, and an approximately model unbiased predictor of the population total is developed. The variance of the prediction error and an approximately unbiased estimator of this variance are derived. The relative efficiency of the model-based predictor with respect to a regression predictor has been estimated, using simulation, both for random generated data and for real data from a business survey. The results indicate that the model predictor is most efficient relative to the regression predictor when a few extremely large elements contribute substantially to the population total.

**Key words:** Superpopulation
Model, Model-based Inference, Outliers, Lognormal Distribution, Auxiliary
variables.

*Last update: 1997-12-16 / KH*