A LARGE-SAMPLE STUDY OF RANK ESTIMATION FOR CENSORED REGRESSION DATA

Large sample approximations are developed to establish asymptotic line arity of the commonly used linear rank estimating functions, defined a s stochastic integrals of counting processes over the whole line, for censored regression data. These approximations lead to asymptotic norm ality of the resulting rank estimators defined as solutions of the lin ear rank estimating equations. A second kind of approximations is also developed to show that the estimating functions can be uniformly appr oximated by certain more manageable nonrandom functions, resulting in a simple condition that guarantees consistency of the rank estimators. This condition is verified for the two-sample problem, thereby extend ing earlier results by Louis and Wei and Gail, as well as in the case when the underlying error distribution has increasing failure rate, wh ich includes most parametric regression models in survival analysis. T echniques to handle the delicate tail fluctuations are provided and di scussed in detail.