Seminar

Functional central limit theorems for single-stage sampling designs

Rik Lopuhaä (Delft University of Technology)

March 30, 2017, 09:30–11:00

Toulouse

Room MS 001

MAD-Stat. Seminar

Abstract

In survey sampling one samples n individuals from a fixed population of size N according to some sampling design, and for each individual in the sample one observes the value of a particular quantity. On the basis of the observed sample, one is interested in estimating population features of this quantity, such as the population total or the population average. Well known estimators for population features that take into account the inclusion probabilities corresponding to the specific sampling design are the Horvitz-Thompson estimator and Hajek's estimator. Distribution theory for these estimators is somewhat limited, partly due to the dependence that is inherent to several sampling designs and partly due to the more complex nature of particular population features. In this talk I will present a number of functional central limit theorems for different types of empirical processes obtained from suitably centering the Horvitz-Thompson and Hajek empirical distribution functions. Basically, these results are obtained merely under conditions on higher order inclusion probabilities corre- sponding to the sampling design at hand. This makes the results generally applicable and allows more complex sampling designs that go beyond the classical simple random sampling or Poisson sampling. As an application I will use the results in combination with the functional delta method to establish the limit distribution of estimators for certain economic indicators, such as the poverty rate and the Gini index. This is joined work with Hélène Boistard and Anne Ruiz-Gazen.