Mathematical Sciences: Inference and Curve-Fitting in Generalizations of Isotonic Regression Models

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Often models fitted to data must obey certain constraints such as monotonicity or monotonicity for individual segments. This research concentrates on statistical modelling when the constraints can be described as either unimodality, piecewise monotonicity, or N-convexity. Fitted functions will come from classes of functions defined by convex cones, unions of several convex cones or intersections of a cone with a linear variety. Computational algorithms will be written, statistical aspects of these procedures will be examined and hypothesis tests will be developed.