A Comparison of Several Robust Estimators for a Finite Population Mean

In survey sampling, ratio and regression estimators are often used to estimate the mean of a finite population. These estimators make use of information on an auxiliary variable that is assumed to be available over the entire population. Generally speaking, the higher the correlation between the response and this auxiliary variable, the more efficient the ratio and regression estimators will be relative to the simple random sample mean. However, these two estimators are quite sensitive to outliers. In the survey sampling context, Chambers (1986) distinguishes between representative and non-representative outliers. The former type of outlier is defined as an observation with similar counterparts in the non-sampled portion of the population, while the latter is unique. Most research on outlier-robust alternatives to the ratio and regression estimators tends to focus on representative outliers. In this paper, we compare via a simulation study the performance of a number of these alternatives under the presence of representative and non-representative outliers, including those based on M-, GM-, and least absolute value L1 estimators considered by Bassett and Saleh (1994). We also extend MM-estimators (see Yohai 1987) to the survey sampling context, and evaluate their performance as well.