Abstract

In data analysis, we must be conscious of the probability density function of population distribution. Then it is a problem why the probability density function is expressed. The estimation of a probability density function based on a sample of independent identically distributed observations is essential in a wide range of applications. The estimation method of probability density function — (1)a parametric method (2)a nonparametric method and (3)a semi-parametric method etc. — it is. In this paper, GMM problem is taken up as a semi-parametric method and We use a wavelet method as a powerful new technique. Compactly supported wavelets are particularly interesting because of their natural ability to represent data with intrinsically local properties.

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