Hilbert space methods are an alternative to the measure-theoretic definitions of random-variables. They are important in the theory of martingales and stochastic integration, as well as in interpolation and density estimation.

This monograph arose out of a desire to develop an approach to statistical infer ence that would be both comprehensive in its treatment of statistical principles and sufficiently powerful to be applicable to a variety of important practical problems. In the latter category, the problems of inference for stochastic processes (which arise com monly in engineering and biological applications) come to mind. Classes of estimating functions seem to be promising in this respect. The monograph examines some of the consequences of extending standard concepts of ancillarity, sufficiency and complete...