Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling
In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different...
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| Format: | Article |
| Language: | English |
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University of Tehran
2013-03-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
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| Online Access: | https://jsciences.ut.ac.ir/article_31923_6ffab824d9a053a13108a5d09cad8ebb.pdf |
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| author | M. Ajami V. Fakoor S. Jomhoori |
| author_facet | M. Ajami V. Fakoor S. Jomhoori |
| author_sort | M. Ajami |
| collection | DOAJ |
| description | In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by real automobile brake pads data. |
| format | Article |
| id | doaj-art-2cd69fcb1a1a471aaf55c9b10b914d18 |
| institution | DOAJ |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2013-03-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-2cd69fcb1a1a471aaf55c9b10b914d182025-08-20T03:08:50ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142013-03-01241556231923Some Asymptotic Results of Kernel Density Estimator in Length-Biased SamplingM. Ajami0V. Fakoor1S. Jomhoori2Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of IranDepartment of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of IranDepartment of Statistics, Faculty of Sciences, University of Birjand, Birjand, Islamic Republic of IranIn this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by real automobile brake pads data.https://jsciences.ut.ac.ir/article_31923_6ffab824d9a053a13108a5d09cad8ebb.pdfasymptotic normalitylength-biasedstrong consistencystrong gaussian approximation |
| spellingShingle | M. Ajami V. Fakoor S. Jomhoori Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling Journal of Sciences, Islamic Republic of Iran asymptotic normality length-biased strong consistency strong gaussian approximation |
| title | Some Asymptotic Results of Kernel Density
Estimator in Length-Biased Sampling |
| title_full | Some Asymptotic Results of Kernel Density
Estimator in Length-Biased Sampling |
| title_fullStr | Some Asymptotic Results of Kernel Density
Estimator in Length-Biased Sampling |
| title_full_unstemmed | Some Asymptotic Results of Kernel Density
Estimator in Length-Biased Sampling |
| title_short | Some Asymptotic Results of Kernel Density
Estimator in Length-Biased Sampling |
| title_sort | some asymptotic results of kernel density estimator in length biased sampling |
| topic | asymptotic normality length-biased strong consistency strong gaussian approximation |
| url | https://jsciences.ut.ac.ir/article_31923_6ffab824d9a053a13108a5d09cad8ebb.pdf |
| work_keys_str_mv | AT majami someasymptoticresultsofkerneldensityestimatorinlengthbiasedsampling AT vfakoor someasymptoticresultsofkerneldensityestimatorinlengthbiasedsampling AT sjomhoori someasymptoticresultsofkerneldensityestimatorinlengthbiasedsampling |