Date: 2016-01-22

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Influential units are those which make classical estimators (e.g., the Horvitz-Thompson estimator or calibration estimators) very unstable. The problem of influential units is particularly important in business surveys, which collect economic variables, whose distribution are highly skewed (heavy right tail). In this talk, we will attempt to answer the following questions:

(1) What is an influential value in surveys? (2) How measure the influence of unit? (3) How reduce the impact of influential units at the estimation stage?

To measure the influence of unit, we use the concept of conditional bias and argue that it is an appropriate influence measure since it accounts for the sampling design, the type of parameter to be estimated and the type of estimator. Using the conditional bias, we propose a general robust estimator, which possesses the desirable feature of being applicable with arbitrary sampling designs. For stratified simple random sampling, it is essentially equivalent to the estimator Kokic and Bell (1994). The proposed robust estimator involves a $\Psi$-function, which depends on a tuning constant. We propose a method for determining the tuning constant, which consists of minimizing the maximum estimated conditional bias. We show that the resulting robust estimator is design-consistent. The implementation of the estimator will be also discussed. Finally, the results of an empirical study, which compares several estimators in terms of bias and relative efficiency, will be presented.

Speaker

David Haziza is a professor of statistics at the Université de Montréal. His main research area is survey sampling.