  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.
