Simulation Comparison Between an Outlier Resistant Model-Based Finite Population Estimator and Design-Based Estimators under Contamination

There are two approaches to finite population estimation. One assumes the finite population elements are fixed quantities. The randomness associated with estimators comes from the random selection of samples. Each sampled element has a weight determined by the sample design, see Cochran (1977) [2]. Most Bureau of Labor Statistics surveys rely on this theory, for example, the Occupational Employment Statistics program which was discussed in depth in Li (2002) [10] about methods used in small area estimation. The other approach assumes the population elements are a random draw from a larger population or “super-population”, in a way similar to taking random samples from a random variable. The random variable has its own mean and variance structure, usually expressed in terms of linear models. Finite population summaries of the variable under investigation, such as mean, total are estimated through fitting sample data to the linear model. The design of the sample selection is relevant only to the selection of a suitable linear model under the “super-population”, but is irrelevant to how the estimates are derived from the model. The first approach is known as “design-based”, the second “model-based”. Särndal, Swensson and Wretman (1992) [14] discusses this distinction in greater detail. Table 1 lists some familiar design-based estimators and their model-based equivalents. A broader review on this connection is in Li (2001) [9]. Since least squares linear estimators are very vulnerable to outlying observations, that is, a small variation in outlying observation produces larger variation in the estimate than non-outlying observations, we desire a model-based estimator that is less responsive to outliers while being efficient. This is especially necessary for survey data since processing error occur prominently in surveys. This study aims to investigate the statistical quality of such a modelbased, outlier insensitive finite population estimator