Regression of ranked responses when raw responses are censored

2016/02/24 by Michael Donohue, Michael C. Donohue, Anthony Gamst +7
Mathematics · #Advanced Statistical Methods and Models #Applications (stat.AP) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference #Survey Sampling and Estimation Techniques #stat.AP #stat.ME

paper · pdf · doi:10.48550/arxiv.1602.07559

33 pages, 6 figures

arxiv created 2016/02/24 · openalex publication_date 2016/02/24 · arxiv updated 2016/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We discuss semiparametric regression when only the ranks of responses are observed. The model is Y_i = F (x_i'\boldsymbolβ₀ + ε_i), where Y_i is the unobserved response, F is a monotone increasing function, x_i is a known p-vector of covariates, \boldsymbolβ₀ is an unknown p-vector of interest, and ε_i is an error term independent of x_i. We observe \(x_i,R_n(Y_i)) : i = 1,… ,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.

Citations

• A Limited Memory Algorithm for Bound Constrained Optimization

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