The radial wavelet frame density estimator

The estimation of probability densities is one of the fundamental problems in scientific research. It has been shown that Wavelet Density Estimators, which are a well-documented nonparametric approach, outperform other nonparametric estimators in problems involving densities with discontinuities and local features. However, the use of this type of estimators is not widely extended in the scientific community mainly because of their heavy computational complexity and their difficult algorithmic implementation. A novel multidimensional Wavelet Density Estimator approach based on new multidimensional scaling functions with analytic closed-form expressions is proposed. The key advantages of the proposed estimator are its simpler multidimensional algorithmic implementation and its significant reduction in computational complexity. Algorithmic formulations for four different data analysis scenarios are presented: (1) batch processing of input data, (2) online estimation for stationary process, (3) online estimation for non-stationary contexts and (4) batch estimation of high-dimensional data. The assessment results show that the proposed approach reduces the computational time of the estimation process while maintaining competitive estimation errors.