Generalized Deconvolution Estimation by Multiwavelets

Based on the generalized deconvolution model, this paper constructs the corresponding multiwavelet estimator, and studies its optimal estimation of the point-wise risk under the local regularization condition. Firstly, the corresponding multiwavelet estimator is constructed by combining the noise information; secondly, the upper bound of point-wise risk between density function and corresponding multiwavelet estimator in local regular space is studied; then, the adaptive multiwavelet estimator is constructed by using data-driven method and its convergence order is studied; finally, the optimality of multiwavelet estimator and data-driven estimator is discussed.

Automated summary

Based on the generalized deconvolution model, this paper constructs the corresponding multiwavelet estimator and studies its optimal estimation of point-wise risk under local regularization condition. The multiwavelet estimator is constructed by combining noise information and the upper bound of point-wise risk between density function and corresponding multiwavelet estimator in local regular space is studied. An adaptive multiwavelet estimator is constructed using a data-driven method and its convergence order is also studied. Finally, the optimality of the multiwavelet estimator and the data-driven estimator is discussed.