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• W2019963506 abstract "Abstract Important order restrictions and general log-linear models for multinomial experiments can often be expressed by requiring that the vector composed of the logs of the probabilities fall within a closed convex cone. Here we exhibit a duality relationship (by way of a Fenchel duality theorem) between these types of problems and projections in I-divergence geometry. We show that many cone-constrained maximum likelihood estimation problems are exactly equivalent to an I projection onto a translation of the negative polar cone. This duality relationship permits the concise characterization of cone-restricted maximum likelihood estimates and the use of iterative algorithms proposed by Csiszar (1975) and Dykstra (1985b), which are analogous to the iterative proportional-fitting procedure. Computational aspects of maximum likelihood estimates are discussed, and a relationship with least squares projections onto isotonic cones is presented. We discuss examples in detail to exhibit the usefulness and power..." @default.
• W2019963506 created "2016-06-24" @default.
• W2019963506 creator A5032780876 @default.
• W2019963506 creator A5070549676 @default.
• W2019963506 date "1988-06-01" @default.
• W2019963506 modified "2023-10-17" @default.
• W2019963506 title "Duality ofIProjections and Maximum Likelihood Estimation for Log-Linear Models Under Cone Constraints" @default.
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• W2019963506 doi "https://doi.org/10.1080/01621459.1988.10478631" @default.
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