Regression of ranked responses when raw responses are censored

TL;DR

This paper develops a semiparametric regression method that estimates relationships between covariates and responses using only response ranks, introducing a novel estimator and demonstrating its theoretical properties and practical application.

Contribution

The paper proposes a new estimator for rank-based semiparametric regression models and establishes its consistency and asymptotic normality under Gaussian assumptions.

Findings

Estimator performs well in simulations

Method applied successfully to Alzheimer's biomarker data

Theoretical properties proven for the estimator

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.