Credibility, Hypothesis Testing and Regression Software

Greg Taylor

ASTIN Bulletin, 2007, vol. 37, issue 2, 517-535

Abstract: It has been known since Zehnwirth (1977) that a scalar credibility coefficient is closely related to the F-statistic of an analysis of variance between and within risk clauses. The F-statistic may also be viewed as testing a certain regression structure, associated with credibility framework, against the null hypothesis of a simpler structure. This viewpoint is extended to multi-dimensional credibility frameworks in which the credibility coefficient is a matrix (Sections 3 and 4), and to hierarchical regression credibility frameworks (Section 6). In each case the credibility coefficient is expressed in terms of the F-statistic that tests the significance of a defined regression structure against a simpler one. Section 5 points out how the computation may be implemented in certain cases by means of regression software.

Date: 2007
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