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We discuss semiparametric regression when only the ranks of responses areobserved. The model is $Y_i = F (\mathbf{x}_i'{\boldsymbol\beta}_0 +\varepsilon_i)$, where $Y_i$ is the unobserved response, $F$ is a monotoneincreasing function, $\mathbf{x}_i$ is a known $p-$vector of covariates,${\boldsymbol\beta}_0$ is an unknown $p$-vector of interest, and$\varepsilon_i$ is an error term independent of $\mathbf{x}_i$. We observe$\{(\mathbf{x}_i,R_n(Y_i)) : i = 1,\ldots ,n\}$, where $R_n$ is the ordinalrank function. We explore a novel estimator under Gaussian assumptions. Wediscuss the literature, apply the method to an Alzheimer's disease biomarker,conduct simulation studies, and prove consistency and asymptotic normality.

Regression of ranked responses when raw responses are censored