Operator on Operator Regression in Quantum Probability

Abstract

This article introduces operator on operator regression in quantum probability. Here in the regression model, the response and the independent variables are certain operator valued observables, and they are linearly associated with unknown scalar coefficient (denoted by $\beta$), and the error is a random operator. In the course of this study, we propose a quantum version of a class of estimators (denoted by $M$ estimator) of $\beta$, and the large sample behaviour of those quantum version of the estimators are derived, given the fact that the true model is also linear and the samples are observed eigenvalue pairs of the operator valued observables.