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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.09278 |
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| _version_ | 1866909735463157760 |
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| author | Zhang, Lucas Z. |
| author_facet | Zhang, Lucas Z. |
| contents | Motivated by the orthogonal series density estimation in $L^2([0,1],μ)$, in this project we consider a new class of functions that we call the approximate sparsity class. This new class is characterized by the rate of decay of the individual Fourier coefficients for a given orthonormal basis. We establish the $L^2([0,1],μ)$ metric entropy of such class, with which we show the minimax rate of convergence. For the density subset in this class, we propose an adaptive density estimator based on a hard-thresholding procedure that achieves this minimax rate up to a $\log$ term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09278 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximate Sparsity Class and Minimax Estimation Zhang, Lucas Z. Econometrics Motivated by the orthogonal series density estimation in $L^2([0,1],μ)$, in this project we consider a new class of functions that we call the approximate sparsity class. This new class is characterized by the rate of decay of the individual Fourier coefficients for a given orthonormal basis. We establish the $L^2([0,1],μ)$ metric entropy of such class, with which we show the minimax rate of convergence. For the density subset in this class, we propose an adaptive density estimator based on a hard-thresholding procedure that achieves this minimax rate up to a $\log$ term. |
| title | Approximate Sparsity Class and Minimax Estimation |
| topic | Econometrics |
| url | https://arxiv.org/abs/2508.09278 |