Variance Estimation of Inequality Indexes Via Different Methods in Complex Sampling Design
Erika Antal, Matti Langel, Yves Tillé, Yves Tillé, Yves Tillé
Institute of Statistics, University of Neuchatel, Neuchatel, Switzerland

Most inequality indices are non linear statistics whose distributions are often asymmetric. They are in general estimated by using a complex sampling design and a calibrated estimator. We will survey two methods to construct a confidence interval for these measures: bootstrap and linearization. For linearization, we will discuss the interest of several methods to derive a linearized variable. Next, we will apply them to complex indices like the Zenga index or the Quintile Share Ratio. We will also propose several new bootstrap techniques for complex designs that take the finite population correction into account. We will also show that the estimation of the variance is not the only issue in the construction of reliable confidence intervals and that the skewness of the distribution must also be taken into account.

Keywords: Inequality index; Inference; Sampling design

Biography: Yves Tillé obtained a PhD from the University of Brussels. He is now a professor of the University of Neuchatel