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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.
}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v56n2.23.01}, url = {http://global-sci.org/intro/article_detail/jms/21824.html} }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.