Wavelet Estimation for Regression Convolution Model with Heteroscedastic Errors (Journal of Mathematical Study, 2023)
This paper considers an unknown functional estimation problem in a multidimensional periodic regression convolution model with heteroscedastic errors. Thismodel has potential applications in signal recovery when both noise and blur arepresent in the observed data. Our approach is mainly theoretical, however. We firstpropose a linear wavelet estimator and then discuss the upper bound for its meanintegrated squared error over Besov balls. Moreover, the rate of convergence of thisestimator under pointwise error is considered. A nonlinear wavelet estimator is constructed by using the hard thresholding method for adaptivity purposes. It should bepointed out that the obtained rate of convergence of the nonlinear estimator is kept thesame as the linear one up to a logarithmic term.
Keywords: Nonparametric estimation; regression convolution model; Heteroscedastic errors; wavelets.