Regression of ranked responses when raw responses are censored

We discuss semiparametric regression when only the ranks of responses are observed. The model is Yi = F (x ′ iβ0 + εi), where Yi is the unobserved response, F is a monotone increasing function, xi is a known p−vector of covariates, β0 is an unknown p-vector of interest, and εi is an error term independent of xi. We observe {(xi, Rn(Yi)) : i = 1, . . . , n}, where Rn is the ordinal rank function. We explore a novel estimator under Gaussian assumptions. We discuss the literature, apply the method to an Alzheimer’s disease biomarker, conduct simulation studies, and prove consistency and asymptotic normality.