Application of Quantum Theory to Super-parametric Density Estimation

In this paper, we will discuss how to generalize nonparametric density estimators to MLE parametric estimators. Basing on the Parzen window theory and using the advantages of probability amplitude of quantum theory, we model a nonlinear optimization problem and it is very difficult, if not impossible, to solve the problem. A constructive procedure for solving the nonlinear programming problem is studied. Though it seems to be very complicated, the approach of this paper is simple and comprehensive. More precisely, the lemmas, the theorems and their proofs serve the purpose for mathematical rigor and practical computation. From the numerical results of the paper by Y. -S. Tsai et al. [7], it shows that a new approach of density estimation, super-parametric density estimation, is established completely.