  We show using statistically rigorous arguments that the technique of weak
value amplification (WVA) does not perform better than standard statistical
techniques for the tasks of single parameter estimation and signal detection.
Specifically we prove that post-selection, a necessary ingredient for WVA,
decreases estimation accuracy and, moreover, arranging for anomalously large
weak values is a suboptimal strategy. In doing so, we explicitly provide the
optimal estimator, which in turn allows us to identify the optimal experimental
arrangement to be the one in which all outcomes have equal weak values (all as
small as possible) and the initial state of the meter is the maximal eigenvalue
of the square of the system observable. Finally, we give precise quantitative
conditions for when weak measurement (measurements without post-selection or
anomalously large weak values) can mitigate the effect of uncharacterized
technical noise in estimation.
