Approximate Sparsity Class and Minimax Estimation

Lucas Z. Zhang

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arXiv · 2508.09278

Approximate Sparsity Class and Minimax Estimation

Lucas Z. Zhang

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Abstract

Motivated by the orthogonal series density estimation in $L^2([0,1],\mu)$, 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 $L^2([0,1],\mu)$ 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.

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BibTeX RIS

Lucas Z. Zhang. 2025-08-12. Approximate Sparsity Class and Minimax Estimation. https://arxiv.org/abs/2508.09278

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