Regression of ranked responses when raw responses are censored
Open Access Publications from the University of California

## Regression of ranked responses when raw responses are censored

• Author(s): Donohue, MC
• Gamst, AC
• Rissman, RA
• Abramson, I
• et al.
Abstract

We discuss semiparametric regression when only the ranks of responses are observed. The model is $Y_i = F (\mathbf{x}_i'{\boldsymbol\beta}_0 + \varepsilon_i)$, where $Y_i$ is the unobserved response, $F$ is a monotone increasing 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 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.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.