@Article{JCM-40-108,
author = {Wu , CongWang , Jinru and Zeng , Xiaochen},
title = {Adaptive and Optimal Point-Wise Estimations for Densities in GARCH-Type Model by Wavelets},
journal = {Journal of Computational Mathematics},
year = {2021},
volume = {40},
number = {1},
pages = {108--126},
abstract = {<p style="text-align: justify;">This paper considers adaptive point-wise estimations of density functions in GARCH-type model under the local Hölder condition by wavelet methods. A point-wise lower bound estimation of that model is first investigated; then we provide a linear wavelet estimate to obtain the optimal convergence rate, which means that the convergence rate coincides with the lower bound. The non-linear wavelet estimator is introduced for adaptivity, although it is nearly-optimal. However, the non-linear wavelet one depends on an upper bound of the smoothness index of unknown functions, we finally discuss a data driven version without any assumptions on the estimated functions.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2007-m2020-0109},
url = {http://global-sci.org/intro/article_detail/jcm/19972.html}
}