Estimates of Percentile Regression Lines Using Salary Data

Abstract

In case of contamination, skewness or unequal variances, a nonparametric alternative to least squares regression is considered. In addition, investigators are often more interested in estimates of percentile lines than in the mean regression line. Thus, a modification of Brown-Mood regression is proposed to estimate the (100p) th percentile line α + βx of a random variable. This technique is applied to some data (artificial, but similar to real) relating the salary (y) of a statistics professor and the number (x) of years in rank. The estimates of several of these percentile lines make very good descriptive statistics.