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

Year, pages: 2019, 1485 - 1500

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.

Yu, Y., Liu, X., Liu, L., Liu, W. 2019. On adaptivity of wavelet thresholding estimators with negatively super-additive dependent noise. In Mathematica Slovaca, vol. 69, no.6, pp. 1485-1500. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0324

Yu, Y., Liu, X., Liu, L., Liu, W. (2019). On adaptivity of wavelet thresholding estimators with negatively super-additive dependent noise. Mathematica Slovaca, 69(6), 1485-1500. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0324

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava