Elias S.W. Shiu and Fuk Yum Sing
Abstract
We present a geometric approach to studying greatest accuracy credibility theory. Our main tool is the concept of orthogonal projections. We show, for example, that to determine the Bühlmann credibility premium is to find the coefficients of the minimum-norm vector in an affine space spanned by certain orthogonal random variables. Our approach is illustrated by deriving various common credibility formulas. Several equivalent forms of the credibility factor Z are derived by means of similar triangles.
Key words and phrases: Greatest accuracy credibility theory, Bühlmann credibility premium, credibility factor, affine space, inner product, orthogonal projection, Bühlmann-Straub model
Corresponding Author:
Elias S.W. Shiu
Department of Statistics and Actuarial Science
E-mail: eshiu@stat.uiowa.edu
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