title: RECENT PROGRESS IN THE NONPARAMETRIC ESTIMATION OF MONOTONE CURVES -WITH APPLICATIONS TO BIOASSAY AND ENVIRONMENTAL RISK ASSESSMENT.
abstract: Three recent nonparametric methodologies for estimating a monotone regression functionFand its inverseF-1are (1) the inverse kernel method DNP (Dette et al. (2005), Dette and Scheder (2010)), (2) the monotone spline (Kong and Eubank (2006)) and (3) the data adaptive method NAM (Bhattacharya and Lin (2010), (2011)), with roots in isotonic regression (Ayer et al. (1955), Bhattacharya and Kong (2007)). All three have asymptotically optimal error rates. In this article their finite sample performances are compared using extensive simulation from diverse models of interest, and by analysis of real data. Let there bemdistinct values of the independent variablexamongNobservationsy. The results show that ifmis relatively small compared toNthen generally the NAM performs best, while the DNP outperforms the other methods whenmisO(N) unless there is a substantial clustering of the values of the independent variablex.
authors.affiliation: The University of Arizona and Duke University.
authors.forename: Rabi
authors.initials: R
authors.lastname: Bhattacharya
authors.forename: Lizhen
authors.initials: L
authors.lastname: Lin