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Estimating ordered parameters by linear programming
Authors:Richard W Cottle  Ingram Olkin
Institution:1. Department of Management Science and Engineering, Stanford University, Stanford, CA 94305-4026, USA;2. Department of Statistics, Stanford University, Stanford, CA 94305-4065, USA
Abstract:There are many models that require the estimation of a set of ordered parameters. For example, multivariate analysis of variance often is formulated as testing for the equality of the parameters versus an ordered alternative. This problem, referred to as isotonic inference, constrained inference, or isotonic regression, has led to the development of general solutions, not often easy to apply in special models. In this expository paper, we study the special case of a separable convex quadratic programming problem for which the optimality conditions lead to a readily solved linear complementarity problem in the Lagrange multipliers, and subsequently to an equivalent linear programming problem, whose solution can be used to recover the solution of the original isotonic problem. The method can be applied to estimating ordered correlations, ordered binomial probabilities, ordered Poisson parameters, ordered exponential scale parameters, or ordered risk differences.
Keywords:62F30  60E05  90C20  90C33
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