Robustness properties of a robust PLS regression method

The presence of multicollinearity in regression data is no exception in real life ex-amples. Instead of applying ordinary regression methods, biased regression techniques such as Principal Component Regression and Ridge Regression have been developed to cope with such data sets. In this paper we consider Partial Least Squares (PLS) regres-sion by means of the SIMPLS algorithm. Because the SIMPLS algorithm is based on the empirical variance-covariance matrix of the data and on least squares regression, outliers have a damaging effect on the estimates. To reduce this pernicious effect of outliers, we propose to replace the empirical variance-covariance matrix in SIMPLS by a robust covariance estimator. We derive the influence function of the resulting PLS weight vectors and the regression estimates, and conclude that they will be bounded if the robust covariance estimator has a bounded influence function. Also the breakdown value is inherited from the robust estimator. We illustrate the results using the MCD estimator and the reweighted MCD estimator (RMCD) for low-dimensional data sets. Also some empirical properties are provided for a high-dimensional data set

A proposed framework for backtesting loss given default models

The Basel Accords require financial institutions to regularly validate their loss given default (LGD) models. This is crucial so banks are not misestimating the minimum required capital to protect them against the risks they are facing through their lending activities. The validation of an LGD model typically includes backtesting, which involves the process of evaluating to what degree the internal model estimates still correspond with the realized observations. Reported backtesting examples have typically been limited to simply measuring the similarity between model predictions and realized observations. It is however not straightforward to determine acceptable performance based on these measurements alone. Although recent research led to advanced backtesting methods for PD models, the literature on similar backtesting methods for LGD models is much scarcer. This study addresses this literature gap by proposing a backtesting framework using statistical hypothesis tests to support the validation of LGD models. The proposed statistical hypothesis tests implicitly define reliable reference values to determine acceptable performance and take into account the number of LGD observations, as a small sample may affect the quality of the backtesting procedure. This workbench of tests is applied to an LGD model fitted to real-life data and evaluated through a statistical power analysis