  We discuss the problem of finding the best measurement strategy for
estimating the value of a quantum system parameter. In general the optimum
quantum measurement, in the sense that it maximizes the quantum Fisher
information and hence allows one to minimize the estimation error, can only be
determined if the value of the parameter is already known. A modification of
the quantum Van Trees inequality, which gives a lower bound on the error in the
estimation of a random parameter, is proposed. The suggested inequality allows
us to assert if a particular quantum measurement, together with an appropriate
estimator, is optimal. An adaptive strategy to estimate the value of a
parameter, based on our modified inequality, is proposed.
