In this paper, I propose a semiparametric estimation procedure for the Box–Cox transformation model. I show a global identification result under mild conditions that allow conditional heteroskedastic error terms. The proposed estimator minimizes a second order U‐process and does not require any user‐chosen values such as a smoothing parameter that sometimes induces unstable inference result. With a slight modification, it can also be applied to random censoring which depends on covariates in an arbitrary way. The estimator converges to an asymptotic normal distribution at the rate of and Monte Carlo experiments show adequate finite sample performance.