Union–intersection principle and constrained statistical inference |
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Authors: | Pranab Kumar Sen |
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Institution: | 1. Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599-7420, USA;2. Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599-3260, USA |
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Abstract: | Most statistical models arising in real life applications as well as in interdisciplinary research are complex in their designs, sampling plans, and associated probability laws, which in turn are often constrained by inequality, order, functional, shape or other restraints. Optimality of conventional likelihood ratio based statistical inference may not be tenable here, although the use of restricted or quasi-likelihood has spurred in such environments. S.N. Roy's ingenious union–intersection principle provides an alternative avenue, often having some computational advantages, increased scope of adaptability, and flexibility beyond conventional likelihood paradigms. This scenario is appraised here with some illustrative examples, and with some interesting problems of inference on stochastic ordering (dominance) in parametric as well as beyond parametric setups. |
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Keywords: | 62A10 62A99 62F99 62G99 62H99 |
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