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Approximate Sparsity Class and Minimax Estimation

2025/08/12 by Zhang, Lucas Z.
Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #Econometrics (econ.EM) #FOS: Economics and business #Machine Learning and Algorithms #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2508.09278

openalex publication_date 2025/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by the orthogonal series density estimation in L2([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 L2([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.

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