  Consider a statistical model with an epistemic restriction such that, unlike
in classical mechanics, the allowed distribution of positions is fundamentally
restricted by the form of an underlying momentum field. Assume an agent
(observer) who wishes to estimate the momentum field given information on the
conjugate positions. We discuss a classically consistent, weakly unbiased, best
estimation of the momentum field minimizing the mean squared error, based on
which the abstract mathematical rules of quantum mechanics can be derived. The
results suggest that quantum wave function is not an objective
agent-independent attribute of reality, but represents the agent's best
estimation of the momentum, given the positions, under epistemic restriction.
Quantum uncertainty and complementarity between momentum and position find
their epistemic origin from the trade-off between the mean squared errors of
simultaneous estimations of momentum field and mean position, with the Gaussian
wave function represents the simultaneous efficient estimations, achieving the
Cram\'er-Rao bounds of the associated mean squared errors. We then argue that
unitary time evolution and wave function collapse in measurement are normative
rules for an agent to update her/his estimation given information on the
experimental settings.
