On generalise l'estimateur bien connu de Hill de l'indice d'une fonction de reparatition avec queue de variation reguliere a une estimation de l'indice d'une loi de valeurs extremes. On demontre la convergence et la normalite asymptotique. On utilise l'estimateur pour certaines estimations comme celle d'une quantile elevee et d'un point d'extremite

A moment estimator for the index of an extreme-value distribution

https://wis.kuleuven.be/stat/robust/papers/2004/boxplotCOMPSTAT04.pdf

An adjusted boxplot for skewed distributions

textPaper prepared for the NBER project on “Risks of Financial Institutions”. We benefited from suggestions
and criticism by many participants in the NBER project on “Risks of financial institutions”, in particular by
the organizers Mark Carey (also involving Dean Amel and Allen Berger) and Rene Stulz, by our discussant
Tony Saunders and by Patrick de Fontnouvelle, Gary Gorton, Andy Lo, Jim O’Brien and Eric Rosengren.
Furthermore, we are grateful for comments we received at the 2004 European Finance Association Meetings
in Maastricht, in particular by our discussant Marco da Rin and by Christian Upper, at the 2004 Ottobeuren
seminar in economics, notably the thoughts of our discussant Ernst Baltensberger, of Friedrich Heinemann
and of Gerhard Illing, as well as at seminars of the Max Planck Institute for Research on Collective Goods,
the Federal Reserve Bank of St. Louis, the ECB and the University of Frankfurt. Gabe de Bondt and David
Marques Ibanez supported us enormously in finding yield spread data, Lieven Baele and Richard Stehle
kindly made us aware of pitfalls in Datastream equity data. Very helpful research assistance by Sandrine
Corvoisier, Peter Galos and Marco Lo Duca as well as editorial support by Sabine Wiedemann are gratefully
acknowledged. Any views expressed only reflect those of the authors and should not be interpreted as the
ones of the ECB or the Eurosystem. The views expressed herein are those of the author(s) and do not
necessarily reflect the views of the National Bureau of Economic Research.
This paper derives indicators of the severity and structure of banking system risk from asymptotic
interdependencies between banks’ equity prices. We use new tools available from multivariate
extreme value theory to estimate individual banks’ exposure to each other (“contagion risk”) and to
systematic risk. Moreover, by applying structural break tests to those measures we study whether
capital markets indicate changes in the importance of systemic risk over time. Using data for the
United States and the euro area, we can also compare banking system stability between the two
largest economies in the world. Finally, for Europe we assess the relative importance of cross-border
bank spillovers as compared to domestic bank spillovers. The results suggest, inter alia, that systemic
risk in the US is higher than in the euro area, mainly as cross-border risks are still relatively mild in
Europe. On both sides of the Atlantic systemic risk has increased during the 1990s.

/pdf/banking-system-stability-a-cross-atlantic-perspective-26qce9suwx.pdf

Banking System Stability. A Cross-Atlantic Perspective

Due to published statistical analyses of operational risk data, methodological approaches to the AMA modeling of operational risk can be discussed more in detail. In this paper we raise some issues concerning correlation (or diversification) effects, the use of extreme value theory and the overall quantitative risk management consequences of extremely heavy-tailed data. We especially highlight issues around infinite mean models. Besides methodological examples and simulation studies, the paper contains indications for further research.

/pdf/infinite-mean-models-and-the-lda-for-operational-risk-35822ft1ez.pdf

Infinite-mean models and the LDA for operational risk

Statistical issues arising in modelling univariate extremes of a random sample have been successfully used in the most diverse fields, such as biometrics, finance, insurance and risk theory. Statistics of univariate extremes (SUE), the subject to be dealt with in this review paper, has recently faced a huge development, partially because rare events can have catastrophic consequences for human activities, through their impact on the natural and constructed environments. In the last decades, there has been a shift from the area of parametric SUE, based on probabilistic asymptotic results in extreme value theory, towards semi-parametric approaches. After a brief reference to Gumbel's block methodology and more recent improvements in the parametric framework, we present an overview of the developments on the estimation of parameters of extreme events and on the testing of extreme value conditions under a semi-parametric framework. We further discuss a few challenging topics in the area of SUE. univariate extremes; parametric and semi-parametric approaches; extreme value index and tail parameters; testing issues.

https://hal.archives-ouvertes.fr/hal-01311707/document

Extreme Value Theory and Statistics of Univariate Extremes: A Review

http://www.stat.jyu.fi/icors2005/icorsabstracts/hubert.pdf

A robust estimator for the tail index of Pareto-type distributions

In this paper, we consider the estimation of insurance premiums for excess-of-loss reinsurance policies in excess of a high retention level. Special attention is paid to Wang’s premium principle and heavy-tailed distributions, for which estimators of small exceedance probabilities allow the estimation of reinsurance premiums. Next to the construction of estimators, we also consider the corresponding asymptotic results and illustrate the finite sample behavior through a real insurance application as well as simulations.

On univariate extreme value statistics and the estimation of reinsurance premiums

The objectives of a robust statistical analysis and of an extreme value analysis apparently are contradictory. Where the extreme data are downweighted in robust statistics, these observations receive most attention in an extreme value approach. The most prominent extreme value methods however are constructed on maximum likelihood estimates based on specific parametric models which are fitted to exceedances over large thresholds. So within an extreme value framework some robust algorithms replacing the maximum likelihood part of this methodology can be of use leading to estimates which are less sensitive to few particular observations. This study is motivated by a soil database quality management project, where in the background of Pareto-type tails, automatic identification of suspicious data is needed.

https://wis.kuleuven.be/stat/robust/papers/2004/tailindexICORS2003.pdf

A Robust Estimator of the Tail Index Based on an Exponential Regression Model

Community pharmacies are major contributors to health care systems across the world. Several studies have been conducted to evaluate community pharmacies services in health care. The purpose of this study was to estimate the social and economic benefits of current and potential future community pharmacies services provided by pharmacists in health care in Portugal. The social and economic value of community pharmacies services was estimated through a decision-model. Model inputs included effectiveness data, quality of life (QoL) and health resource consumption, obtained though literature review and adapted to Portuguese reality by an expert panel. The estimated economic value was the result of non-remunerated pharmaceutical services plus health resource consumption potentially avoided. Social and economic value of community pharmacies services derives from the comparison of two scenarios: “with service” versus “without service”. It is estimated that current community pharmacies services in Portugal provide a gain in QoL of 8.3% and an economic value of 879.6 million euros (M€), including 342.1 M€ in non-remunerated pharmaceutical services and 448.1 M€ in avoided expense with health resource consumption. Potential future community pharmacies services may provide an additional increase of 6.9% in QoL and be associated with an economic value of 144.8 M€: 120.3 M€ in non-remunerated services and 24.5 M€ in potential savings with health resource consumption. Community pharmacies services provide considerable benefit in QoL and economic value. An increase range of services including a greater integration in primary and secondary care, among other transversal services, may add further social and economic value to the society.

https://repositorio-aberto.up.pt/bitstream/10216/111669/2/255662.pdf

Social and economic value of Portuguese community pharmacies in health care

Background 
The possibility of incorporating generics into combination antiretroviral therapy and breaking apart once-daily single-tablet regimens (STRs), may result in less efficacious medications and/or more complex regimens with the expectation of marked monetary savings. A modeling approach that assesses the merits of such policies in terms of lifelong costs and health outcomes using adherence and effectiveness data from real-world U.S. settings.


Methods 
A comprehensive computer-based microsimulation model was developed to assess the lifetime health (life expectancy and quality adjusted life-years—QALYs) and economic outcomes in HIV-1 infected patients initiating STRs compared with multiple-table regimens including generic medications where possible (gMTRs). The STRs considered included tenofovir disoproxil fumarate/emtricitabine and efavirenz or rilpivirine or elvitegravir/cobicistat. gMTRs substitutions included each counterpart to STRs, including generic lamivudine for emtricitabine and generic versus branded efavirenz.


Results 
Life expectancy is estimated to be 1.301 years higher (discounted 0.619 QALY gain) in HIV-1 patients initiating a single-tablet regimen in comparison to a generic-based multiple-table regimen. STRs were associated with an average increment of $26,547.43 per patient in medication and $1,824.09 in other medical costs due to longer survival which were partially offset by higher inpatients costs ($12,035.61) with gMTRs treatment. Overall, STRs presented incremental lifetime costs of $16,335.91 compared with gMTRs, resulting in an incremental cost-effectiveness ratio of $26,383.82 per QALY gained.


Conclusions 
STRs continue to represent good value for money under contemporary cost-effectiveness thresholds despite substantial price reductions of generic medications in the U. S.

/pdf/cost-effectiveness-of-single-versus-generic-multiple-tablet-48q9svdjx5.pdf

Björn Vandewalle

Papers

A robust estimator for the tail index of Pareto-type distributions

On univariate extreme value statistics and the estimation of reinsurance premiums

A Robust Estimator of the Tail Index Based on an Exponential Regression Model

Social and economic value of Portuguese community pharmacies in health care

Cost-Effectiveness of Single- Versus Generic Multiple-Tablet Regimens for Treatment of HIV-1 Infection in the United States.