The Estimation Methodology Of Multiwavelet Density Function And Application

Probability density estimation plays an important role in statistics, in both theoretical research and practical application, the probability density estimation is helpful to solve most problems in statistics. It provide more choices to solve the probability density estimation. Base on the orthogonality and local adaptation of wavelet basis, wavelet density estimation has advantages in some aspects than nonparametric density estimation in many aspects, such as processe some signal with local shock or sharp variations in processing signal. Wavelet density estimation provides an effective method to solve the problem of probability density estimation. However, wavelet bases cannot be simultaneously symmetric, orthogonal, and compactly supported. We can choice multiwavelet basis overcome these disadvantages and extend the methodology of wavelet bases to use multiwavelet bases and constructions a new method--multiwavelet density estimation.In this paper, we use multiwavelet bases instead of wavelet bases, on the basis of present foundation of wavelet density estimation, we extend the methodology of wavelet to multiwavelet. Firstly, we deduce the function expression of multiwavelet density estimation, and discuss relevant contents of linear multiwavelet density estimation. Secondly, we discuss the linear form and obtain the rate of convergence which proved that this method is feasible in theory. Thirdly, we make an analogue simulation to deal with experimental data and the experimental result prove the effectiveness of this method.