A MARTINGALE APPROACH TO WEIGHTED APPROXIMATIONS

                   David M. Mason

               University of Delaware

A martingale approach to weighted approximations will be
described. Special cases include the uniform empirical and
quantile processes, the finite sampling process, the rank
statistics process and the weighted bootstrap process.
Special emphasis will be given to a weighted approximation
to a serial rank type process from which the classical rank
tests for serial correlation are formed. An unexpected random
graph structure lurking behind serial ranks points the way to
the necessary martingale. A number of applications to
statistics will be discussed.