# The QUANTLIFE Procedure

### Nelson-Aalen-Type Estimator for Censored Quantile Regression

Peng and Huang (2008) propose a method of censored quantile regression that is based on the Nelson-Aalen estimator of the cumulative hazard function. Let , and . Then the following equation is a martingale process that is associated with the counting process (Fleming and Harrington, 1991):

Based on the martingale process, Peng and Huang (2008) derive the following estimating equation:

where and . By approximating the integral in the estimating equation on a grid , the regression quantiles , , can be estimated sequentially by solving the following linear programming problem:

where

and is the known matrix of ’s. For more information, see Koenker (2008).

You can request this method by specifying the METHOD=NA option. The grid points are equally spaced, with specified by the INITTAU=option and the grid step between two adjacent grid points specified by the GRIDSIZE=option.