A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data
Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed...
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| Format: | Article |
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University of Tehran
2015-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
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| Online Access: | https://jsciences.ut.ac.ir/article_55314_84b4409865483c3736c46be5ce3efb54.pdf |
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| author | P. Asghari V. Fakoor M. Sarmad |
| author_facet | P. Asghari V. Fakoor M. Sarmad |
| author_sort | P. Asghari |
| collection | DOAJ |
| description | Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infinity by a proper choice of the bandwidth.The results of a simulation study is also presented in this paper inorder to examine the performance of the result. |
| format | Article |
| id | doaj-art-cc4f556660ce4c8d8d7d6d1c189b900b |
| institution | Kabale University |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-cc4f556660ce4c8d8d7d6d1c189b900b2025-08-20T03:54:07ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142015-09-0126326527255314A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased DataP. Asghari0V. Fakoor1M. Sarmad2Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran.Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran.Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran.Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infinity by a proper choice of the bandwidth.The results of a simulation study is also presented in this paper inorder to examine the performance of the result.https://jsciences.ut.ac.ir/article_55314_84b4409865483c3736c46be5ce3efb54.pdfasymptotic normalityberry-esseen theoremkernel estimatorrate of convergencelength-biased |
| spellingShingle | P. Asghari V. Fakoor M. Sarmad A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data Journal of Sciences, Islamic Republic of Iran asymptotic normality berry-esseen theorem kernel estimator rate of convergence length-biased |
| title | A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data |
| title_full | A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data |
| title_fullStr | A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data |
| title_full_unstemmed | A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data |
| title_short | A Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data |
| title_sort | berry esseen type bound for the kernel density estimator of length biased data |
| topic | asymptotic normality berry-esseen theorem kernel estimator rate of convergence length-biased |
| url | https://jsciences.ut.ac.ir/article_55314_84b4409865483c3736c46be5ce3efb54.pdf |
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