Robust Hidiroglou-Lavallée Stratified Design

The presence of outliers can strongly bias the sampling design and hence the survey results. In particular, it could induce a wrong computation of the number of statistical units to sample, usually overestimating it. In what follows we focus on the stratified sampling design, which has been proven to be the most efficient surveying technique under some basic assumptions (see Tillé, 2001) and it is currently in use at several NSIs for business surveys. For in-stance, suppose that in the stratification variable X some outliers arise. Outliers are observations arbitrarily far from the majority of the data. They are often due to mis-takes, like editing, measurement and observational errors. Intuitively, when outliers are present in a given stratum for the stratification variable X they affect both the location and scale measures for X. Therefore, it is clear that a higher dispersion than the 'true' one will be observed in that stratum.