Abstract
We propose two simple approaches, the discrete and sieve methods, to estimate the regression-transformation models with heteroscedastic data that assume the existence of an unknown monotone transformation of the lifetime into regression with known distribution of the unknown random error term. Under thicker cutoff points, these two methods can obtain equivalent estimators for the regression coefficients and semiparameter, the transformation function. All of these estimators for the regression coefficients by the two methods are asymptotic unbiased and have the same asymptotic normal distribution with $\sqrt{n}$ convergent rate, and the simulations also show that their power might approach to efficiency. Since it is difficult to show if the empirical ROC estimator proposed by Hsieh (1996) is efficient, the informaton of the ROC method is compared with the discrete and sieve methods in this paper, and simulations show that the ROC method loss some information and it concludes that both the discrete and sieve methods are more applicable than the ROC method.