We discuss semiparametric regression when only the ranks of responses are
observed. The model is Yiβ=F(xiβ²βΞ²0β+Ξ΅iβ), where Yiβ is the unobserved response, F is a monotone
increasing function, xiβ is a known pβvector of covariates,
Ξ²0β is an unknown p-vector of interest, and
Ξ΅iβ is an error term independent of xiβ. We observe
{(xiβ,Rnβ(Yiβ)):i=1,β¦,n}, where Rnβ 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.Comment: 33 pages, 6 figure