LINEARIZATION OF RANDOMLY WEIGHTED EMPIRICALS UNDER LONG RANGE DEPENDENCE WITH APPLICATIONS TO NONLINEAR REGRESSION QUANTILES
研究了长程相依随机变量下随机加权经验过程的渐近一致线性化结果，并用于线性化非线性回归分位数，得到其极限行为，与独立同分布误差情形形成鲜明对比。
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.