Title: The asymptotic distribution of the isotonic regression estimator over a general countable pre-ordered set
Authors: Vladimir Pastukhov - Lund University (Sweden) [presenting]
Dragi Anevski - Lund University (Sweden)
Abstract: The problem of isotonic regression over a general countable pre-ordered set is studied. We prove that the limiting distribution of the isotonised estimator is given by the concatenation of the separate isotonic regressions of the restrictions of an underlying estimators asymptotic distribution to the comparable level sets of the underlying estimators probability limit. Also, we show that the isotonisation preserves the rate of convergence of the underlying estimator. We apply the results to the problems of estimation of a bimonotone regression function and estimation of a bimonotone probability mass function.