Any type of statistical inquiry in business, government, or academics in
which principles from some body of knowledge enter seriously into the
analysis is likely to lead to a nonlinear statistical model. For instance, a
model obtained as the solution of a differential equation arising in engineering,
chemistry, or physics is usually nonlinear. Other examples are economic
models of consumer demand or of intertemporal consumption and
investment.
Much applied work using linear models represents a distortion of the
underlying subject matter. In the past there was little else that one could do,
given the restrictions imposed by the cost of computing equipment and the
lack of an adequate statistical theory. But the availability of computing
resources is no longer a problem, and advances in statistical and probability
theory have occurred over the last fifteen years that effectively remove the
restriction of inadequate theory.
In this book, I have attempted to bring these advances together in one
place, organize them, and relate them to applications, for the use of
students as a text and for the use of those engaged in research as a
reference. My hopes and goals in writing it will be achieved if it becomes
possible for the reader to bring subject matter considerations directly to
bear on data without distortion.