The confidence interval methods in quantum language

TL;DR

This paper explores confidence interval methods through the lens of quantum language, a framework that unifies classical and quantum systems, emphasizing the roles of estimators, quantities, and semi-distances for theoretical understanding.

Contribution

It introduces a novel perspective by applying quantum language to classical confidence interval methods, highlighting three key concepts as essential for their theoretical foundation.

Findings

Reinterprets confidence intervals using quantum language principles

Identifies estimator, quantity, and semi-distance as crucial concepts

Proposes a new theoretical framework aligning with classical statistical methods

Abstract

Recently we proposed quantum language(or, measurement theory), which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. Also, we consider that this is a kind of system theory such that it is applicable to both classical and quantum systems. As far as classical systems, it should be noted that quantum language is similar to statistics. In this paper, we discuss the usual confidence interval methods in terms of quantum language. And we assert that three concepts (i.e.,"estimator" and "quantity" and "semi-distance)are indispensable for the theoretical understanding of the confidence interval methods. Since our argument is quite elementary, we hope that the readers acquire a new viewpoint of statistics, and agree that our proposal is, from the pure theoretical point of view, the true confidence interval methods. (Key words: Confidence interval, Chi-squared distribution, Student's t-distribution)