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Extra resources for A Decision Making Methodology In Support Of The Business Rules Lifecycle.IEEE.1997

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Eo)dv = a. To find a locallj^ most powerful one-sided test (^ > ^o) we maximize 7r'(0o)= j P\XMdv Jw subject to 7r{0i)) = a. Using the Neyman-Pearson Lemma, the optimal region is defined bv 6 C. R. Rao where A is chosen such that the size of the region is a, as shown in Rao and Poti (1946). >A^. 9) m) vm) In the multiparameter case, the slope of the power function in the direction a = (ai,... 8). 1, let the hypothesis to be tested be Ho : h{0) = c, where /i is an r x 1 vector function of the p-vector 9 with p>r and c is a given r-vector of constants.

3b) for prior group. R. A. Abstract: The three asymptotic tests, Neyman and Pearson Likehhood Ratio (LR), Wald's statistic (W) and Rao's score (RS)are referred to in statistical hterature on testing of hypotheses as the Holy Trinity. All these tests are equivalent to the first-order of asymptotics, but differ to some extent in the second-order properties. Some of the merits and defects of these tests are presented. Some applications of the score test, recent developments on refining the score test and problems for further investigation are presented.

In considering the score statistic, Rao (1948) used the ml estimates of parameters. A similar theory can be developed using BAN estimators. 6. Rao (1951) suggested the use of score tests in sequential analysis for testing a simple null versus a simple alternative hypothesis. Bradley (1953) considered a nice application of Rao's sequential test in clinical trials. An appUcation in quality control is given by Box and Ramirez (1992). For some comments on sequential score test and possible applications reference may be made to Sen (1997).

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