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...
Saved in:
| Main Author: | |
|---|---|
| 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 |