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Abstract
The generalised score and Wald tests are described and related to their nongeneralised versions. Two interesting applications are discussed. In the first a new test for the Behrens-Fisher problem is derived. The second is testing homogeneity of variances from multiple univariate normal populations.
Highlights
This paper is intended to be a tutorial for those wishing to inform themselves about the generalised score and Wald Tests
By not preferred we mean that, for example, estimates may be calculated by some iterative scheme with dubious convergence
Other possibilities are that estimates may have a convoluted expression or the finite sample properties such as large bias may be inappropriate for the problem of interest
Summary
This paper is intended to be a tutorial for those wishing to inform themselves about the generalised score and Wald Tests. It extends the content of 1 and has similar objectives; that is, it focuses on the use of these tests rather than their properties. When ML estimation under one of the null and full models is not preferred, the likelihood ratio test is problematic, but one of the score and Wald tests is not. When ML estimation under both the null and full models is not preferred, we need another way forward This is provided by the generalised score and Wald Tests.
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