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Bayesian and Maximum Likelihood Approaches to Order Restricted
A Method of Finding Projections Onto the Intersection of Convex
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Adaptive test algorithm applied asymptotic Barlow Bartholomew Bayes block Brunk Chi-Bar-Square test coefficients computed Conditional test consider constraints contrast test convergence convex convex cone corresponding criterion defined denote density estimator Department of Statistics distribution function Dykstra equations exponential exponential family four-moment approximation GCV's given Hence inequality isopleth isopleth form isotonic regression kurtosis large values least squares Lemma likelihood ratio test linear M-estimator Math matrix maximized maximum likelihood estimates means methods minimize ML estimates nonnegative nonparametric normal distribution null distribution null hypothesis obtain order restricted inference order statistics ordered alternatives parameters partitioning pooling power function probability problem procedure projections PROOF rank RC model reject Robertson and Wright robust sample sizes Section sequence sigmoid simple tree simulation solution sets space Statistical Inference Table test statistics testing H_ tests based Theorem two-moment unimodal University of Iowa variance vector violator zero