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 ness into this setting. The reader should note that the
development is mathematically "mature" in its use of Hilbert space
methods but not, we believe, mathematically difficult. This is in
keeping with our desire to construct a theory that is rich in
statistical tools for infer ence without the difficulties found in
modern developments, such as likelihood analysis of stochastic
processes or higher order methods, to name but two. The fundamental
notions of orthogonality and projection are accessible to a good
undergraduate or beginning graduate student. We hope that the
monograph will serve the purpose of enriching the methods available
to statisticians of various interests."
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