Monotone rank estimation of transformation models with length-biased and right-censored data

This paper considers the monotonic transformation model with an unspecified transformation function and an unknown error function, and gives its monotone rank estimation with length-biased and right-censored data. The estimator is shown to be root n-consistent and asymptotically normal. Numerical simulation studies reveal good finite sample performance and the estimator is illustrated with the Oscar data set. The variance can be estimated by a resampling method via perturbing the U-statistics objective function repeatedly.