Dirichlet kernel density estimation for strongly mixing sequences on the simplex
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914136393252864 |
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| author | Daayeb, Hanen Khardani, Salah Ouimet, Frédéric |
| author_facet | Daayeb, Hanen Khardani, Salah Ouimet, Frédéric |
| contents | This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong mixing conditions. We establish rigorous results for the asymptotic normality and mean squared error of these estimators, extending previous findings from the independent and identically distributed (iid) context to the more general setting of strongly mixing processes. To demonstrate its practical utility, the estimator is applied to monthly market-share compositions of several Renault vehicle classes over a twelve-year period, with bandwidth selection performed via leave-one-out least squares cross-validation. Our findings underscore the reliability and strength of Dirichlet kernel techniques when applied to temporally dependent compositional data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_08816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dirichlet kernel density estimation for strongly mixing sequences on the simplex Daayeb, Hanen Khardani, Salah Ouimet, Frédéric Statistics Theory Methodology 62G07, 60G10, 60F05, 62G05, 62G20, 62H10, 62H20 This paper investigates the theoretical properties of Dirichlet kernel density estimators for compositional data supported on simplices, for the first time addressing scenarios involving time-dependent observations characterized by strong mixing conditions. We establish rigorous results for the asymptotic normality and mean squared error of these estimators, extending previous findings from the independent and identically distributed (iid) context to the more general setting of strongly mixing processes. To demonstrate its practical utility, the estimator is applied to monthly market-share compositions of several Renault vehicle classes over a twelve-year period, with bandwidth selection performed via leave-one-out least squares cross-validation. Our findings underscore the reliability and strength of Dirichlet kernel techniques when applied to temporally dependent compositional data. |
| title | Dirichlet kernel density estimation for strongly mixing sequences on the simplex |
| topic | Statistics Theory Methodology 62G07, 60G10, 60F05, 62G05, 62G20, 62H10, 62H20 |
| url | https://arxiv.org/abs/2506.08816 |