Graduation: some experiments with kernel methods

Abstract

It may be useful to begin with some introductory comments on the nature of graduation and its uses with particular reference to the distinction between graduation by parametric methods, as described in traditional actuarial textbooks, and graduation by non-parametric methods.Some of the comments have appeared in the early sections of Copas and Haberman's paper which first described the kernel method of non-parametric graduation.Graduation may be regarded as the principles by which a set of data is adjusted in order to provide a basis suitable for inferences to be drawn and further practical calculations to be made. In actuarial terminology, graduation usually refers to a set of decremental rates, and one of the principal actuarial examples of its use is the construction of a life table from a set of age-specific, observed death rates.