An Improved Model for Kernel Density Estimation Based on Quadtree and Quasi-Interpolation

There are three main problems for classical kernel density estimation in its application: boundary problem, over-smoothing problem of high (low)-density region and low-efficiency large samples. A new improved model multivariate adaptive binned quasi-interpolation based on a quadtree algorithm is proposed, which can avoid the deficiency improve precision model. The constructed steps. Firstly, threshold set from dimensions sample number, width bins kurtosis, bounded domain adaptively partitioned into several non-intersecting (intervals) by using iteration idea algorithm. Then, good properties quasi-interpolation, functions introducing theory quasi-interpolation. Finally, coefficients frequency replacing probability. Simulation Monte Carlo method shows that proposed non-parametric effectively solve shortcomings significantly prediction accuracy calculation efficiency function