Model-based Outlier Treatment in Business Surveys: Estimating the Population Total Using a Multivariate Lognormal Model

 by Forough Naderi

 Research Report 1995:7

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


An estimator of the population total of a variable, using information from arbitrarily many auxiliary variables, is developed. The estimator is based on the assumption that the variables follow a multivariate lognormal distribution. The behaviour of the estimator under lognormality is examined for various parameter combinations, and it is found to be more efficient than a (design-based) regression estimator. A large number of sample drawings from a set of random multivariate lognormal data are used in order to confirm that the bias is negligible under lognormality. Sample drawings from an observed material is used in order to see how the estimator performs in practice. The bias of the estimator is high when applied to the material, but it is nonetheless far more efficient than the regression estimator for small sample sizes. It is concluded that the bias is due to the fact that the material is not perfectly lognormal. A modified estimation procedure, in which the logarithmed observations are weighted by a potency of the unlogarithmed values, is investigated. The estimator improves considerably when using the modified procedure.

 Key words: Outlier, Multivariate Lognormal distribution, Model-based estimation, Weight. 

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Last update: 1997-12-16 / KH