Statistical Inverse Problem

TL;DR

This paper introduces a new root density estimator with optimal asymptotic properties for statistical data analysis, specifically addressing the inverse problem in quantum mechanics by estimating the psi function from experimental data.

Contribution

It develops a novel root density estimator that can be applied to quantum inverse problems, advancing the methodology for distribution density estimation.

Findings

The root density estimator exhibits optimal asymptotic behavior.

The method effectively estimates the psi function from experimental data.

Applicable to quantum mechanics inverse problems.

Abstract

A fundamental problem of statistical data analysis, distribution density estimation by experimental data, is considered. A new method with optimal asymptotic behavior, the root density estimator, is developed. The method proposed may be applied to its full extent to solve the statistical inverse problem of quantum mechanics, namely, estimating the psi function on the basis of the results of mutually complementing experiments.