Adaptive Density Estimation Using Projection Kernels and Penalized Comparison to Overfitting
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| Format: | Preprint |
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2025
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| _version_ | 1866915486882594816 |
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| author | Hoang, Van Ha Nguyen, Tien Dat Nguyen, Thi Mong Ngoc |
| author_facet | Hoang, Van Ha Nguyen, Tien Dat Nguyen, Thi Mong Ngoc |
| contents | In this work, we study wavelet projection estimators for density estimation, focusing on their construction from $\mathcal{S}$-regular, compactly supported wavelet bases. A key aspect of such estimators is the choice of the resolution level, which controls the balance between bias and variance. To address this, we employ the Penalized Comparison to Overfitting (PCO) method, providing a fully data-driven selection of the multiresolution level. This approach ensures both statistical accuracy and computational feasibility, while retaining the adaptability of wavelet methods. Our results establish an oracle inequality for the proposed estimator and show that it attains the optimal rate of convergence in density estimation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Density Estimation Using Projection Kernels and Penalized Comparison to Overfitting Hoang, Van Ha Nguyen, Tien Dat Nguyen, Thi Mong Ngoc Statistics Theory 62G07, 62G20, 62G05 In this work, we study wavelet projection estimators for density estimation, focusing on their construction from $\mathcal{S}$-regular, compactly supported wavelet bases. A key aspect of such estimators is the choice of the resolution level, which controls the balance between bias and variance. To address this, we employ the Penalized Comparison to Overfitting (PCO) method, providing a fully data-driven selection of the multiresolution level. This approach ensures both statistical accuracy and computational feasibility, while retaining the adaptability of wavelet methods. Our results establish an oracle inequality for the proposed estimator and show that it attains the optimal rate of convergence in density estimation. |
| title | Adaptive Density Estimation Using Projection Kernels and Penalized Comparison to Overfitting |
| topic | Statistics Theory 62G07, 62G20, 62G05 |
| url | https://arxiv.org/abs/2509.07800 |