Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data

The purpose of this paper is to provide some asymptotic results for nonparametric estimator of the Lorenz curve and Lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. First, we show that nonparametric estimator of the Lorenz curve is uniforml...

Full description

Saved in:
Bibliographic Details
Main Author: M. Bolbolian Ghalibaf
Format: Article
Language:English
Published: University of Tehran 2012-06-01
Series:Journal of Sciences, Islamic Republic of Iran
Subjects:
Online Access:https://jsciences.ut.ac.ir/article_25070_453a46e5e4cb607054363a5d4a914521.pdf
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849730540701220864
author M. Bolbolian Ghalibaf
author_facet M. Bolbolian Ghalibaf
author_sort M. Bolbolian Ghalibaf
collection DOAJ
description The purpose of this paper is to provide some asymptotic results for nonparametric estimator of the Lorenz curve and Lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. First, we show that nonparametric estimator of the Lorenz curve is uniformly strongly consistent for the associated Lorenz curve. Also, a strong Gaussian approximation for the associated Lorenz process is established under appropriate assumptions. Using this strong Gaussian approximation, a law of the iterated logarithm for the Lorenz process is also derived.
format Article
id doaj-art-caad225f542c4dff9febc72e4cb300ae
institution DOAJ
issn 1016-1104
2345-6914
language English
publishDate 2012-06-01
publisher University of Tehran
record_format Article
series Journal of Sciences, Islamic Republic of Iran
spelling doaj-art-caad225f542c4dff9febc72e4cb300ae2025-08-20T03:08:50ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142012-06-0123217117725070Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent DataM. Bolbolian Ghalibaf0Department of Statistics, School of Mathematical Sciences and Computer, Hakim Sabzevari Univercity,The purpose of this paper is to provide some asymptotic results for nonparametric estimator of the Lorenz curve and Lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. First, we show that nonparametric estimator of the Lorenz curve is uniformly strongly consistent for the associated Lorenz curve. Also, a strong Gaussian approximation for the associated Lorenz process is established under appropriate assumptions. Using this strong Gaussian approximation, a law of the iterated logarithm for the Lorenz process is also derived.https://jsciences.ut.ac.ir/article_25070_453a46e5e4cb607054363a5d4a914521.pdflaw of the iterated logarithmstrong gaussian approximationlorenz curvestrong mixingtruncated data
spellingShingle M. Bolbolian Ghalibaf
Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data
Journal of Sciences, Islamic Republic of Iran
law of the iterated logarithm
strong gaussian approximation
lorenz curve
strong mixing
truncated data
title Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data
title_full Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data
title_fullStr Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data
title_full_unstemmed Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data
title_short Asymptotic Behaviors of the Lorenz Curve for Left Truncated and Dependent Data
title_sort asymptotic behaviors of the lorenz curve for left truncated and dependent data
topic law of the iterated logarithm
strong gaussian approximation
lorenz curve
strong mixing
truncated data
url https://jsciences.ut.ac.ir/article_25070_453a46e5e4cb607054363a5d4a914521.pdf
work_keys_str_mv AT mbolbolianghalibaf asymptoticbehaviorsofthelorenzcurveforlefttruncatedanddependentdata