Tom Reynkens

Sparse PCA for High-Dimensional Data With Outliers

A new sparse PCA algorithm is presented, which is robust against outliers. The approach is based on the ROBPCA algorithm that generates robust but nonsparse loadings. The construction of the new ROSPCA method is detailed, as well as a selection criterion for the sparsity parameter. An extensive simulation study and a real data example are performed, showing that it is capable of accurately finding the sparse structure of datasets, even when challenging outliers are present. In comparison with a projection pursuit-based algorithm, ROSPCA demonstrates superior robustness properties and comparable sparsity estimation capability, as well as significantly faster computation time.

Modelling censored losses using splicing: a global fit strategy with mixed Erlang and extreme value distributions

In risk analysis, a global fit that appropriately captures the body and the tail of the distribution of losses is essential. Modeling the whole range of the losses using a standard distribution is usually very hard and often impossible due to the specific characteristics of the body and the tail of the loss distribution. A possible solution is to combine two distributions in a splicing model: a light-tailed distribution for the body which covers light and moderate losses, and a heavy-tailed distribution for the tail to capture large losses. We propose a splicing model with a mixed Erlang (ME) distribution for the body and a Pareto distribution for the tail. This combines the flexibility of the ME distribution with the ability of the Pareto distribution to model extreme values. We extend our splicing approach for censored and/or truncated data. Relevant examples of such data can be found in financial risk analysis. We illustrate the flexibility of this splicing model using practical examples from risk measurement.

Fitting tails affected by truncation

In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as the Gutenberg-Richter relation in geophysics, while at other instances the nature of the measurement process itself may cause under recovery of large values, for instance due to flooding in river discharge readings. Recently Beirlant et al. (2016) discussed tail fitting for truncated Pareto-type distributions. Using examples from earthquake analysis, hydrology and diamond valuation we demonstrate the need for a unified treatment of extreme value analysis for truncated heavy and light tails. We generalise the classical Peaks over Threshold approach for the different max-domains of attraction with shape parameter

Hunting for Black Swans in the European Banking Sector Using Extreme Value Analysis

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Estimating the maximum possible earthquake magnitude using extreme value methodology: the Groningen case

to allow for truncation effects. We use a pseudo-maximum likelihood approach to estimate the model parameters and consider extreme quantile estimation and reconstruction of quantile levels before truncation whenever appropriate. We report on some simulation experiments and provide some basic asymptotic results.

Sparse Regression with Multi-type Regularized Feature Modeling.

In financial risk management, a Black Swan refers to an event that is deemed improbable yet has massive consequences. In this communication we propose a way to investigate if the recent financial crisis was a Black Swan event for a given bank based on weekly closing prices and derived log-returns. More specifically, using techniques from extreme value methodology we estimate the tail behavior of the negative log-returns over two specific horizons: Pre-crisis: from January 1, 1994 until August 7, 2007 (often referred to as the official starting date of the credit crunch crisis); Post-crisis: from August 8, 2007 until September 23, 2014 (the cut-off date of our study).

Estimating the Maximum Possible Earthquake Magnitude Using Extreme Value Methodology: The Groningen Case

The area-characteristic, maximum possible earthquake magnitude

Actuarial and statistical aspects of reinsurance in R

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