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CONSTRAINED MAXIMUM LIKELIHOOD ESTIMATION OF N STOCHASTICALLY ORDERED DISTRIBUTIONS,
RAND CORP SANTA MONICA CALIF
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A consideration is made of the problem of determining step function maximum likelihood estimates for N stochastically ordered distributions, subject to the constraint that the estimates themselves must also be stochastically ordered. Brunk and others achieved a closed form solution for the case where N equals 2, but they were unable to extend the results to the case where N is greater than 2. This study presents a new analytical method based on the Kuhn-Tucker optimality conditions for the equivalent concave program. For N equal to 2, the method yields the closed form solution of Brunk. When used in conjunction with a reduction strategy previously developed by the author, the method yields an efficient computational algorithm for N equal to or greater than three. Computational experience shows that large problems can be solved in reasonable time with good accuracy, especially when compared with the performance of a general nonlinear programming algorithm applied directly to the equivalent concave program. Author
APPROVED FOR PUBLIC RELEASE