SMALL AREA ESTIMATION FOR SKEWED DATA IN THE PRESENCE OF ZEROES

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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability

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ISSN: 1234-7655
eISSN: 2450-0291

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VOLUME 16 , ISSUE 4 (December 2015) > List of articles

SMALL AREA ESTIMATION FOR SKEWED DATA IN THE PRESENCE OF ZEROES

Forough Karlberg *

Keywords : small area estimation, representative outliers, zero-valued observations, lognormal-logistic mixture model.

Citation Information : Statistics in Transition New Series. Volume 16, Issue 4, Pages 541-562, DOI: https://doi.org/10.21307/stattrans-2015-032

License : (CC BY 4.0)

Published Online: 01-November-2017

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ABSTRACT

Skewed distributions with representative outliers pose a problem in many surveys. Various small area prediction approaches for skewed data based on transformation models have been proposed. However, in certain applications of those predictors, the fact that the survey data also contain a non-negligible number of zero-valued observations is sometimes dealt with rather crudely, for instance by arbitrarily adding a constant to each value (to allow zeroes to be considered as “positive observations, only smaller”, instead of acknowledging their qualitatively different nature). On the other hand, while a lognormal-logistic model has been proposed (to incorporate skewed distributions as well as zeroes), that model does not include any hierarchical aspects, and is therefore not explicitly adapted to small area prediction. In this paper, we consolidate the two approaches by extending one of the already established log-transformation mixed small area prediction models to incorporate a logistic component. This allows for the simultaneous, systematic treatment of domain effects, outliers and zero-valued observations in a single framework. We benchmark the resulting model-based predictors (against relevant alternatives) in applications to simulated data as well as empirical data from the Australian Agricultural and Grazing Industries Survey.

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