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 rightcensored data. The estimator is shown to be √ 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.Keywords monotone rank estimation, length-biased data, right-censored data, random weighting, transformation model
MSC(2010) 62F10, 62F12, 62F40Citation: Chen X P, Shi J H, Zhou Y. Monotone rank estimation of transformation models with length-biased and right-censored data.