On adaptivity of wavelet thresholding estimators with negatively super-additive dependent noise

2019/10/09 by Yuncai Yu, Yu, Yuncai, Xinsheng Liu +5
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #62C20 #62G07 #62G08 #62G10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability and Risk Models #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1910.03911

openalex publication_date 2019/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers the nonparametric regression model with negatively super-additive dependent (NSD) noise and investigates the convergence rates of thresholding estimators. It is shown that the term-by-term thresholding estimator achieves nearly optimal and the block thresholding estimator attains optimal (or nearly optimal) convergence rates over Besov spaces. Additionally, some numerical simulations are implemented to substantiate the validity and adaptivity of the thresholding estimators with the presence of NSD noise.

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