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Weak approximations for empirical Lorenz curves and their Goldie inverses of stationary observations

Part of: Limit theorems Nonparametric inference

Published online by Cambridge University Press:  01 July 2016

Miklós Csörgő  and
Hao Yu
Miklós Csörgő*
Affiliation:
Carleton University
Hao Yu*
Affiliation:
The University of Western Ontario
*
∗ Postal address: Department of Mathematics and Statistics, Carleton University, Ottawa, Ont., Canada, K1S 5B6.
∗∗ Postal address: Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, Ont., Canada, N6A 5B7. Email address: hyu@fisher.stats.uwo.ca
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Abstract

By using Chibisov-O'Reilly type theorems for uniform empirical and quantile processes based on stationary observations, we establish a weak approximation theory for empirical Lorenz curves and their inverses used in economics. In particular, we obtain weak approximations for empirical Lorenz curves and their inverses also under the assumptions of mixing dependence, often used structures of dependence for observations.

Keywords

Lorenz curveinverse Lorenz curveempirical Lorenz processempirical concentration processempirical processquantile processweighted metricstationaritymixing

MSC classification

Primary: 62G05: Estimation
Secondary: 60F17: Functional limit theorems; invariance principles
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 3 , September 1999 , pp. 698 - 719
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

Supported by an NSERC Canada grant at Carleton University, Ottawa, Canada.

Supported by an NSERC Canada grant of M. Csörgő and an NSERC Canada grant at the University of Western Ontario.

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