Regression of ranked responses when raw responses are censored

Abstract

We discuss semiparametric regression when only the ranks of responses are observed. The model is $Y_i=F({\mathbf{x}}_i^{\prime }{\mathbf{\beta }}_0+{\epsilon }_i)$, where $Y_i$ is the unobserved response, $F$ is a monotone increasing function, ${\mathbf{x}}_i$ is a known $p-$vector of covariates, ${\mathbf{\beta }}_0$ is an unknown $p$-vector of interest, and ${\epsilon }_i$ is an error term independent of ${\mathbf{x}}_i$. We observe $\{({\mathbf{x}}_i,R_n(Y_i)):i=1,\dots ,n\}$, where $R_n$ 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.

33 pages, 6 figures