On kernel mode estimation under RLT and WOD model
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| Format: | Preprint |
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2024
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| _version_ | 1866910782423302144 |
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| author | Alem, Mohamed Kaber El Guessoum, Zohra Tatachak, Abdelkader |
| author_facet | Alem, Mohamed Kaber El Guessoum, Zohra Tatachak, Abdelkader |
| contents | Let $(X_N)_{N\geq 1}$ denote a sequence of real random variables and let $\vartheta$ be the mode of the random variable of interest $X$. In this paper, we study the kernel mode estimator (say) $\vartheta_n$ when the data are widely orthant dependent (WOD) and subject to Random Left Truncation (RLT) mechanism. We establish the uniform consistency rate of the density estimator (say) $f_n$ of the underlying density $f$ as well as the almost sure convergence rate of $\vartheta_n$. The performance of the estimators are illustrated via some simulation studies and applied on a real dataset of car brake pads. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_07874 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On kernel mode estimation under RLT and WOD model Alem, Mohamed Kaber El Guessoum, Zohra Tatachak, Abdelkader Statistics Theory 62G20 (Primary), 62G05 (Secondary) G.3 Let $(X_N)_{N\geq 1}$ denote a sequence of real random variables and let $\vartheta$ be the mode of the random variable of interest $X$. In this paper, we study the kernel mode estimator (say) $\vartheta_n$ when the data are widely orthant dependent (WOD) and subject to Random Left Truncation (RLT) mechanism. We establish the uniform consistency rate of the density estimator (say) $f_n$ of the underlying density $f$ as well as the almost sure convergence rate of $\vartheta_n$. The performance of the estimators are illustrated via some simulation studies and applied on a real dataset of car brake pads. |
| title | On kernel mode estimation under RLT and WOD model |
| topic | Statistics Theory 62G20 (Primary), 62G05 (Secondary) G.3 |
| url | https://arxiv.org/abs/2412.07874 |