  Weak-value amplification (WVA) has recently become an important technique for
parameter estimation, owing to its ability to enhance the signal-to-noise ratio
by amplifying extremely small signals with proper postselection strategies. In
this paper, we propose an adaptive WVA scheme to achieve the highest Fisher
information when using an unbalanced pointer. Different from previous schemes,
the adaptive WVA scheme is associated with a real-time update on the
postselection states with the help of feedback information from the outcomes,
and the "extremely small" condition set on the parameter of interest is
relaxed. By applying this scheme to a time-delay measurement scenario, we show
by numerical simulation that the precision achieved in our scheme is several
times higher than the standard WVA scheme. Our result might open a path for
improving the WVA technique in a more flexible and robust way.
