Finding an unknown number of multivariate outliers

We use the forward search to provide robust Mahalanobis distances to detect the presence of outliers in a sample of multivariate normal data. Theoretical results on order statistics and on estimation in truncated samples provide the distribution of our test statistic. We also introduce several new robust distances with associated distributional results. Comparisons of our procedure with tests using other robust Mahalanobis distances show the good size and high power of our procedure. We also provide a unification of results on correction factors for estimation from truncated samples

Backtesting Expected Shortfall: a simple recipe?

We propose a new backtesting framework for Expected Shortfall that could be used by the regulator. Instead of looking at the estimated capital reserve and the realised cash-flow separately, one could bind them into the secured position, for which risk measurement is much easier. Using this simple concept combined with monotonicity of Expected Shortfall with respect to its target confidence level we introduce a natural and efficient backtesting framework. Our test statistics is given by the biggest number of worst realisations for the secured position that add up to a negative total. Surprisingly, this simple quantity could be used to construct an efficient backtesting framework for unconditional coverage of Expected Shortfall in a natural extension of the regulatory traffic-light approach for Value-at-Risk. While being easy to calculate, the test statistic is based on the underlying duality between coherent risk measures and scale-invariant performance measures

Semi-nonparametric Estimation of Operational Risk Capital with Extreme Loss Events

Bank operational risk capital modeling using the Basel II advanced measurement approach (AMA) often lead to a counter-intuitive capital estimate of value at risk at 99.9% due to extreme loss events. To address this issue, a flexible semi-nonparametric (SNP) model is introduced using the change of variables technique to enrich the family of distributions to handle extreme loss events. The SNP models are proved to have the same maximum domain of attraction (MDA) as the parametric kernels, and it follows that the SNP models are consistent with the extreme value theory peaks over threshold method but with different shape and scale parameters from the kernels. By using the simulation dataset generated from a mixture of distributions with both light and heavy tails, the SNP models in the Frechet and Gumbel MDAs are shown to fit the tail dataset satisfactorily through increasing the number of model parameters. The SNP model quantile estimates at 99.9 percent are not overly sensitive towards the body-tail threshold change, which is in sharp contrast to the parametric models. When applied to a bank operational risk dataset with three Basel event types, the SNP model provides a significant improvement in the goodness of fit to the two event types with heavy tails, yielding an intuitive capital estimate that is in the same magnitude as the event type total loss. Since the third event type does not have a heavy tail, the parametric model yields an intuitive capital estimate, and the SNP model cannot provide additional improvement. This research suggests that the SNP model may enable banks to continue with the AMA or its partial use to obtain an intuitive operational risk capital estimate when the simple non-model based Basic Indicator Approach or Standardized Approach are not suitable per Basel Committee Banking Supervision OPE10 (2019).Comment: There are 32 pages, including tables, figures, appendix and reference. The research was presented at the MATLAB Annual Computational Finance Conference, September 27-30, 202

Particle Identification with Energy Loss in the CMS Silicon Strip Tracker

Some complementary methods are proposed for an identification of charged particles based on $dE/dx$ in the silicon microstrip modules of the CMS Tracker. The performance of proton selection is discussed as benchmark, and the impact of the main systematic effects is estimated. Strategies are presented for the validation and calibration of the methods with several categories of data