A new algorithm for computing quantile regression estimates for proble
ms in which the response function is nonlinear in parameters is descri
bed. The nonlinear I, estimation problem is a special (median) case. T
he algorithm is closely related to recent developments on interior poi
nt methods for solving linear programs. Performance of the algorithm o
n a variety of test problems including the censored linear quantile re
gression problem of Powell (1986) is reported.