Abstract
The population parameters based on Gini were introduced in previous chapters. One of the objectives in practice is to estimate them from a given data set. This is the main objective of this chapter. When dealing with estimation, several issues come in mind. Is the data based on individual observations or are they grouped? Is the sampling procedure based on equal probability or is it a stratified one? Are the variables of interest coming from a continuous or a discrete distribution? The estimation procedures depend on the answers to the above questions. In addition, the Gini-based parameters have various presentations which lead to different estimators, each one being the natural estimator of a specific definition.
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Notes
- 1.
Gini (1914, reprinted 2005) was well aware of this problem. The way he corrected it was by presenting both the diagonal and the Lorenz curve as step functions. However, because the convexity/concavity of the Lorenz curve carries important information concerning the properties of the random variables it seems that this approach is not very useful because of the properties we are interested in.
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Yitzhaki, S., Schechtman, E. (2013). Inference on Gini-Based Parameters: Estimation. In: The Gini Methodology. Springer Series in Statistics, vol 272. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4720-7_9
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