On Goodness of Fit for Operational Risk

The Advanced Measurement Approach (AMA) to operational risk, as described by the Basel Committee on Banking Supervision ( 2011 ), provides a framework meant to be used by banks for establishing the capital required to be set aside to cover worst‐case operational loss scenarios. The problems raised by an AMA approach are primarily statistical in nature, and many lie at the frontier of statistical research. The aim of this paper is to contribute to one of the more pressing challenges of an AMA, namely that of testing the goodness of fit (GoF) of a distributional family to operational loss data. Our focus is on extending certain classically known tests, such as that of Anderson–Darling, with particular emphasis on the right tails of the distributions. The nature of such GoF tests is examined in detail, and computational efficiency of the procedures is taken into account. We also propose a novel saddlepoint approximation method for assessing the asymptotic null distributions of the test statistics based on the eigenvalues of covariance kernels estimated via a jackknife and influence function‐based approach.