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DENSITY SMOOTHNESS PARAMETER ESTIMATION WITH SOME ADDITIVE NOISES

  • Zhao, Junjian (Department of Mathematics College of Science Tianjin Polytechnic University) ;
  • Zhuang, Zhitao (College of Mathematics and Information Science North China University of Water Resources and Electric Power)
  • Received : 2017.03.28
  • Accepted : 2017.11.07
  • Published : 2018.10.31

Abstract

In practice, the density function of a random variable X is always unknown. Even its smoothness parameter is unknown to us. In this paper, we will consider a density smoothness parameter estimation problem via wavelet theory. The smoothness parameter is defined in the sense of equivalent Besov norms. It is well-known that it is almost impossible to estimate this kind of parameter in general case. But it becomes possible when we add some conditions (to our proof, we can not remove them) to the density function. Besides, the density function contains impurities. It is covered by some additive noises, which is the key point we want to show in this paper.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

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