On the convergence rate in the central limit theorem for linearly extended negative quadrant dependent random variables and its applications
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915502521057280 |
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| author | Alem, Mohamed Kaber El Guessoum, Zohra Tatachak, Abdelkader Sadki, Ourida |
| author_facet | Alem, Mohamed Kaber El Guessoum, Zohra Tatachak, Abdelkader Sadki, Ourida |
| contents | In this paper, we establish the convergence rate in central limit theorem (CLT) for linearly extended negative quadrant dependent (LENQD) random variables (rv's). Under some weak conditions, the rate of normal approximation is shown as $O(n^{-1/9})$. As an application, the convergence rate in CLT of the wavelet estimator for the nonparametric regression model with LENQD errors is presented as $O(n^{-1/9})$. The performance of the main results is illustrated through a simulation study based on a real dataset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15353 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the convergence rate in the central limit theorem for linearly extended negative quadrant dependent random variables and its applications Alem, Mohamed Kaber El Guessoum, Zohra Tatachak, Abdelkader Sadki, Ourida Statistics Theory Primary 60F05, Secondary 62G20 G.3 In this paper, we establish the convergence rate in central limit theorem (CLT) for linearly extended negative quadrant dependent (LENQD) random variables (rv's). Under some weak conditions, the rate of normal approximation is shown as $O(n^{-1/9})$. As an application, the convergence rate in CLT of the wavelet estimator for the nonparametric regression model with LENQD errors is presented as $O(n^{-1/9})$. The performance of the main results is illustrated through a simulation study based on a real dataset. |
| title | On the convergence rate in the central limit theorem for linearly extended negative quadrant dependent random variables and its applications |
| topic | Statistics Theory Primary 60F05, Secondary 62G20 G.3 |
| url | https://arxiv.org/abs/2509.15353 |