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Wavelet optimal estimations for a two-dimensional continuous-discrete density function over risk
Lin Hu1, Xiaochen Zeng2, Jinru Wang2
11Department of Basic Courses, Beijing Union University, Beijing, P.R. China.
Abstract:
The mixed continuous-discrete density model plays an important role in reliability, finance, biostatistics, and economics. Using wavelets methods, Chesneau, Dewan, and Doosti provide upper bounds of wavelet estimations on risk for a two-dimensional continuous-discrete density function over Besov spaces . This paper deals with ( ) risk estimations over Besov space, which generalizes Chesneau-Dewan-Doosti's theorems. In addition, we firstly provide a lower bound of risk. It turns out that the linear wavelet estimator attains the optimal convergence rate for , and the nonlinear one offers optimal estimation up to a logarithmic factor.
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