Understanding influential observations in regression estimation of finite population means using graphs

Auxiliary information plays a central role in estimating parameters of a finite population from survey data. Suppose the turnover mean over firms in a region is of concern, the knowledge of the mean number of employees could be used in the analysis to obtain a more efficient survey strategy. Moreover, regression estimation is a powerful technique to account for such auxiliary information. Besides, the presence of observations, which might be considered somehow different from the others, contributes to the mean of the survey variable in the population. The presence of such observations in the selected sample has, thus, to be taken into account with respect to the influence on both the bias and the variability of an estimator. In this paper we attempt to assess and visualize, by means of the forward search, the influence of individual observations in the efficiency of different regression estimators of the mean.