Walter Maffenini

The possibility of analysing the inequality of a frequency distribution through a point measure is undoubtedly an advantage for any socioeconomic research. The Lorenz curve is the cornerstone on which other global inequality measures have been subsequently introduced...

Being temporarily not at home can often cause the impossibility to give out a questionnaire to each selected unit of a sample; moreover, a high percentage of nonrespondents can strongly affect the quality of estimates. In order to solve this problem the ‘‘not at home’’ are usually called back until they become available; however, this methodology highly increases the costs of a survey. The main idea of this paper traces back to an estimation method early proposed by Politz and Simmons; in particular, a new estimator, based on the regression method, is proposed, so that the auxiliary information about the number of evenings spent at home by the units of the target population can be used. The proposed estimator is shown to be unbiased and more efficient than the one based only on the responses of the units being at home when first contacted. Moreover, unlike from the Politz-Simmons estimator, the variance of the proposed estimator can be easily determined and computed. Finally, in order to discuss the asymptotic properties of the regression estimator, the results of some simulations are reported; both the proposed estimator and the Politz-Simmons one turn out to be asymptotically unbiased; however, the regression estimator still proves to be more efficient.

The sample mean difference  is an unbiased estimator of Gini’s mean difference A. It is well known that  is asymptotically normally distributed (Hoeffding, 1948). In order to obtain confidence intervals for A,  must be standardized and hence its variance Var(Â) must be estimated. In this paper we study the effective coverage of the confidence intervals for A, when using a specific unbiased estimator ^ Var(Â) for the variance of Â, in a non-parametric framework. The empirical determination of the minimum sample size required to reach a good approximation of the nominal coverage is analyzed through a new approach. The reported results show that this threshold is critically related to the asymmetry and the tail heaviness in the underlying distribution.

In this paper, the bipolar mean, that can be seen as a frequencies distribution, has been extended to the discrete variables.