This paper discusses some asymptotic uniform linearity results of randomly
weighted empirical processes based on long range dependent random variables+
These results are subsequently used to linearize nonlinear regression quantiles in
a nonlinear regression model with long range dependent errors, where the design
variables can be either random or nonrandom+ These, in turn, yield the limiting
behavior of the nonlinear regression quantiles+ As a corollary, we obtain the limiting
behavior of the least absolute deviation estimator and the trimmed mean
estimator of the parameters of the nonlinear regression model+ Some of the limiting
properties are in striking contrast with the corresponding properties of a
nonlinear regression model under independent and identically distributed error
random variables+ The paper also discusses an extension of rank score statistic in
a nonlinear regression model+