Optimum: minimax estimation of quadratic functionals for quadratically constrained signal classes

A new procedure for the minimax estimation of quadratic functionals of signals is described. The estimates are optimum when the signals satisfy a quadratic constraint, a common assumption made for estimation of linear functionals. The method will, for example, provide best minimax estimates of signal energy in a time-window and of pointwise evaluations of Fourier transform magnitude, in contrast to earlier methods, which first obtain optimum minimax estimates of linear functionals, and subsequently form a suboptimum quadratic estimate by evaluating a weighted sum of the squared linear estimates