Title: “Unlinked monotone regression”.

Abstract : We consider so-called univariate unlinked regression when the unknown regression curve is monotone. In standard monotone regression, one observes a pair (X;Y) where a response Y is linked to a covariate X through the model Y = m(X) + e, with m the (unknown) monotone regression function and e the unobserved error assumed to be independent of X. In the unlinked regression setting one gets only to observe a vector of realizations from both the covariate X and the response Y that is only assumed to have the same distribution as m(X) + e. There is no (observed) pairing of X and Y and the two sample sizes could even be different. Despite this, it is actually still possible to derive a consistent non-parametric estimator of m under the assumption of monotonicity of m and knowledge of the distribution of the noise. Joint work with Fadoua Balabdaoui (Seminar fur Statistik, ETH, Zurich) and  Charles R. Doss (School of Statistics, University of Minnesota).