@Article{JMS-56-2,
author = {Christophe, Chesneau and Kou, Junke},
title = {Wavelet Estimation for Regression Convolution Model with Heteroscedastic Errors},
journal = {Journal of Mathematical Study},
year = {2023},
volume = {56},
number = {2},
pages = {111--134},
abstract = {<p style="text-align: justify;">This paper considers an unknown functional estimation problem in a multidimensional periodic regression convolution model with heteroscedastic errors. This
model has potential applications in signal recovery when both noise and blur are
present in the observed data. Our approach is mainly theoretical, however. We first
propose a linear wavelet estimator and then discuss the upper bound for its mean
integrated squared error over Besov balls. Moreover, the rate of convergence of this
estimator under pointwise error is considered. A nonlinear wavelet estimator is constructed by using the hard thresholding method for adaptivity purposes. It should be
pointed out that the obtained rate of convergence of the nonlinear estimator is kept the
same as the linear one up to a logarithmic term.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v56n2.23.01},
url = {https://global-sci.com/article/87619/wavelet-estimation-for-regression-convolution-model-with-heteroscedastic-errors}
}