Order Restricted Statistical Inference.

Thomas J. Santner; Tim Robertson; F. T. Wright; R. L. Dykstra

doi:10.2307/2289813

June 1, 1990Journal of the American Statistical Association

Order Restricted Statistical Inference.

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Key Points

To establish a theoretical and methodological framework for statistical inference under order and shape restrictions on parameters.
Synthesizes isotonic regression methods and hypothesis testing frameworks for ordered normal means.
Extends likelihood ratio tests and related procedures to multinomial parameters and distributions subject to shape constraints.
Applies conditional expectation over sigma-lattices to characterize geometric projection methods in generalized settings.
Provides analytical formulations and test statistics for ordered hypotheses across normal, multinomial, and generalized distributions.
Establishes duality principles and geometric projection properties that govern parameter estimation under order constraints.

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Implication

Methodological review demonstrates frameworks for order-restricted inference and isotonic regression across probability distributions, highlighting enhanced statistical power for constrained data.

Abstract

Isotonic Regression. Tests of Ordered Hypotheses: The Normal Means Case. Tests of Ordered Hypotheses: Generalizations of the Likelihood Ratio Tests and Other Procedures. Inferences about a Set of Multinomial Parameters. Duality. Inferences Regarding Distributions Subject to Shape Restrictions. Conditional Expectation Given a sigma-lattice: Projections in a More General Setting. Complements. Tables. Bibliography and Related References. Index. Symbols and Acronyms.

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Santner et al. (1990) studied this question.

synapsesocial.com/papers/6a0db606cecdf5fb20ba92d9 https://doi.org/10.2307/2289813

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Order Restricted Statistical Inference.

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Implication

Abstract

Discussion

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Order Restricted Statistical Inference.

Key Points

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Implication

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