In this thesis, optimal power allocation problems are investigated for vector parameter estimation according to various Fisher information based optimality criteria. By considering a generic observation model involving a linear/nonlinear transformation of the parameter vector and an additive noise component with an arbitrary joint probability distribution, six different optimal power allocation problems are formulated based on Fisher information based objective functions. Various closed-form solutions are derived for the proposed problems using opti-mization theoretic approaches for the cases in which the transformation acting on the parameter vector is linear. Also, the results are extended to cases in which nuisance parameters exist in the system model, and to the cases when the transformation acting on the parameter vector is nonlinear. It is shown that the proposed methods are also valid for the provided extensions under certain conditions. Numerical examples are presented to investigate performance of the proposed power allocation strategies, and it is shown that they provide significant performance gains over the equal power allocation strategy.