Mathematical Sciences: Statistical Inference Under PatternedAlternatives Based on the Principle of Isotonic Regression

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This research deals with statistical inference concerning hypotheses in which a vector of parameters is contained in a union of cones defined by order restrictions. Such constraints arise naturally when the parameters are known to follow a pattern. The aim of the research is to extend the theory of isotonic regression, which is used in order restricted inference, to this more general setting. Three specific approaches are proposed. The first involves modifying algorithms used for calculating the isotonic regression of a vector. The second is to investigate the distributional properties of test statistics based on contrasts, including a simultaneous multiple comparison procedure. This research in the theory of statistical inference is a major effort in a current thrust to create statistics that are valid when the variable of interest is ordered. The current state of the art in statistical inference assumes the variable to be categorial or continuous. This research aims to extend statistics to a large class of variables for which there is not a rigorous theory.