Simultaneous confidence bands for isotonic functions

Procedures for simultaneous confidence bands are provided for bivariate regression data {chi,Y(chi),chi is an element of x}, where EY(chi) is an unknown monotonic function of x. A new bandwidth procedure is introduced which generalizes the previously introduced procedures of Korn [1982. Confidence bands for isotonic dose-response curves. Appl. Statist. 31, 59-63] and Lee [1996. On estimation for monotone dose-response curves. J. Amer. Statist. Assoc. 91, 1110-1119]. To gain insight into the comparability and applicability of these procedures a unifying geometric framework is used. This framework leads to certain optimality results for these banding procedures and allows for extensions to settings that have not been previously considered. (c) 2008 Elsevier B.V. All rights reserved.