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|Title:||Improving Inadmissible Hypothesis Testing Procedures in Exponential Family Statistical Models (Lrt, Pointwise Compactness, One-Sided Alternatives)|
|Author(s):||Al-Rawwash, Hussein Moh'd|
|Department / Program:||Statistics|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Abstract:||This thesis is devoted to constructing tests of hypotheses that dominate a given test which violates certain conditions such as convexity or monotonicity. Many authors, for example, Birnbaum (1955), Matthes and Truax (1967), Ferguson (1967), Eaton (1970) and Marden (1981), (1982), have worked on this type of testing problem. They found that a necessary condition for a test to be admissible is that its acceptance region should satisfy certain convexity and monotonicity conditions. These results are not constructive, however, to the extent that one does not know what test(s) dominate a given inadmissible one.
In this thesis the researcher provides a method of constructing a test which strictly dominates one that violates the convexity or the monotonicity conditions. The construction method exploits the case where the parameter is real valued, in which case Ferguson's (1967) construction in one dimension can be used by conditioning on the sufficient statistics of the nuisance parameters. A sequence of tests can be obtained iteratively, each one strictly dominating the previous test. The convergence of this sequence is investigated. It is shown that the relative convex hulls of the acceptance regions decrease. The researcher can only conjecture that the limiting test is "best" in the sense that it can not be improved any further. The conjecture is solved for the case of a discrete dominating measure.
Moreover, the Likelihood Ratio Test (L.R.T.) conjecture, proposed by J. Marden in an NSF proposal (1982), is addressed and partially solved in this thesis. The L.R.T. conjecture states that the more restrictions which are put on the alternative space, the higher the power of the L.R.T.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1986.
|Date Available in IDEALS:||2014-12-16|