Jürg Hüsler - Academia.edu (original) (raw)

Papers by Jürg Hüsler

Communications in Statistics, Apr 22, 2011

In this article, we introduce a new estimator for the generalized Pareto distribution, which is b... more In this article, we introduce a new estimator for the generalized Pareto distribution, which is based on the maximum likelihood estimation and the goodness of fit. The asymptotic normality of the new estimator is shown and a small simulation. From the simulation, the performance of the new estimator is roughly comparable with maximum likelihood for positive values of the shape parameter and often much better than maximum likelihood for negative values.

Extremes, Oct 28, 2006

Let X 1 , X 2 , ..., X n be independent identically distributed random variables with common dist... more Let X 1 , X 2 , ..., X n be independent identically distributed random variables with common distribution function F, which is in the max domain of attraction of an extreme value distribution, i.e., there exist sequences a n > 0 and b n ∈ R such that the limit of P(a −1 n (max 1≤i≤n X i − b n) ≤ x) exists. Assume the density function f (of F) exists. We obtain an uniformly weighted approximation to the tail density function f , and an uniformly weighted approximation to the tail density function of P(a −1 n (max 1≤i≤n X i − b n) ≤ x) under some second order condition.

Communications in Statistics, May 4, 2016

ABSTRACT When a distribution function is in the max domain of attraction of an extreme value dist... more ABSTRACT When a distribution function is in the max domain of attraction of an extreme value distribution, its tail can be well approximated by a generalized Pareto distribution. Based on this fact we use a moment estimation idea to propose an adapted maximum likelihood estimator for the extreme value index, which can be understood as a combination of the maximum likelihood estimation and moment estimation. Under certain regularity conditions, we derive the asymptotic normality of the new estimator and investigate its �nite sample behavior by comparing with several classical or competitive estimators. A simulation study shows that the new estimator is competitive with other estimators in view of average bias, average MSE and coe�cient of variance of the new device for the optimal selection of the threshold. (accepted)

Methodology and Computing in Applied Probability, Feb 28, 2008

Let Y i , 1 ≤ i ≤ n be i.i.d. random variables with the generalized Pareto distribution W γ,σ wit... more Let Y i , 1 ≤ i ≤ n be i.i.d. random variables with the generalized Pareto distribution W γ,σ with γ < 0. We define the empirical mean excess process with respect to {Y i , 1 ≤ i ≤ n} as in Eq. 2.1 (see below) and investigate its weak convergence. As an application, two new estimators of the negative tail index γ are constructed based on the linear regression to the empirical mean excess function and their consistency and asymptotic normality are obtained. Keywords Mean excess function • Tail index • Linear regression • Empirical mean excess process • Goodness-of-fit test AMS 2000 Subject Classification 62G32 • 60G70 F n (a n x + b n) → G γ (x) := exp −(1 + γ x) −1/γ

Statistics & Probability Letters, May 1, 2006

In this paper we present the weighted least squares estimator for the extreme value index, and pr... more In this paper we present the weighted least squares estimator for the extreme value index, and prove its consistency and asymptotic normality.

Birkhäuser eBooks, 2007

Rolf-Dieter Reiss Michael Thomas FB Mathematik Universität Siegen Walter-Flex-Str. 3 57068 Siegen... more Rolf-Dieter Reiss Michael Thomas FB Mathematik Universität Siegen Walter-Flex-Str. 3 57068 Siegen Germany e-mail: reiss@stat.math.uni-siegen.de michael@stat.math.uni-siegen.de 2000 Mathematics Subject Classiﬁcation 60G70, 62P05, 62P99, 90A09, 62N05, 68N15, 62-07, ...

Statistics & Probability Letters, 2011

Extreme shock models have been introduced in Gut and Hüsler (1999) to study systems that at rando... more Extreme shock models have been introduced in Gut and Hüsler (1999) to study systems that at random times are subject to shock of random magnitude. These systems break down when some shock overcomes a given resistance level. In this paper we propose an alternative approach to extreme shock models using reinforced urn processes. As a consequence of this we are able to look at the same problem under a Bayesian nonparametric perspective, providing the predictive distribution of systems' defaults.

Methodology and Computing in Applied Probability

We study the limiting behaviour of the maximum of a bivariate (finite or infinite) moving average... more We study the limiting behaviour of the maximum of a bivariate (finite or infinite) moving average model, based on discrete random variables. We assume that the bivariate distribution of the iid innovations belong to the Anderson's class (Anderson, 1970). The innovations have an impact on the random variables of the INMA model by binomial thinning. We show that the limiting distribution of the bivariate maximum is also of Anderson's class, and that the components of the bivariate maximum are asymptotically independent.

The International Journal of Prosthodontics

The aim of the present study was to assess the perceptibility and acceptability threshold values ... more The aim of the present study was to assess the perceptibility and acceptability threshold values for color differentiation at the restoration and mucosa levels. Materials and Methods: One restored single-tooth implant and the contralateral reference tooth were spectrophotometrically assessed in 20 patients. Perceptibility and acceptability were evaluated by dentists, dental technicians, and laypeople. Results: Dental technicians had the highest sensitivity in the perception of tooth color differences (∆E = 2.7), followed by dentists (∆E = 3.3) and laypeople (∆E = 4.4). Acceptability threshold values were generally higher than perceptibility threshold in all groups. Dental technicians exhibited the highest sensitivity in the perception of mucosa color differences (50% perceptibility at ∆E = 2.65), followed by dentists (∆E > 3.7) and laypeople (∆E > 6). Conclusion: Color differences were tolerated with varying degrees among the three groups. Laypeople accepted higher color differences at the mucosa level.

The International Journal of Prosthodontics, 2021

To evaluate the minimum ceramic thickness needed to increase the lightness by one value by means ... more To evaluate the minimum ceramic thickness needed to increase the lightness by one value by means of glass-ceramic restorations, as perceived by dental technicians, dentists, and laypersons. Materials and Methods: A total of 15 assessment pairs (= reference and test sample) were formed using glass-ceramic blocks in four different colors. Each assessment pair was comprised of two underground blocks differing by one value of lightness. On top of the underground blocks, glass-ceramic platelets were cemented in 5 different thicknesses (0.1 to 0.5 mm) in the same color as the reference. Dental technicians, dentists, and laypersons (n = 41/group) were asked to determine the presence of a color difference between the two samples under standardized light conditions. The threshold ceramic thickness was defined as the thickness at which ≥ 50% of the evaluators were not able to perceive a difference within an assessment pair. The thresholds were analyzed, and groups were compared by applying chi-square test (P < .05). Results: The majority of dentists and dental technicians (> 50%) detected a lightness difference between test and reference samples up to a ceramic thickness of 0.5 mm. The majority of laypersons (≥ 50%) did not perceive lightness differences with ceramic thicknesses of 0.5 mm. If separated by the different color changes, the threshold ceramic thickness started at 0.4 mm and varied within the groups of evaluators and the lightness of the assessed color. Conclusions: A considerable number of evaluators perceived a lightness difference when minimally invasive ceramic restorations of 0.5-mm thickness were applied. The threshold ceramic thickness, however, was reduced when the lightness of the substrate was lower.

Zeitschrift für Orthopädie und Unfallchirurgie, 2007

Schmerzen sind Hauptsymptom degenerativer Gelenkerkrankungen und auch fester Bestandteil der meis... more Schmerzen sind Hauptsymptom degenerativer Gelenkerkrankungen und auch fester Bestandteil der meisten Patientenfragebogen, wie SF-36, WOMAC und weiteren [1, 2]. Die Schmerzmessung im Alltag und in der Medizin sind unter-schiedlich. Im Alltag wird die Stärke mit Worten ausgedrückt und in den allermeisten Studien werden die Schmerzen mit Zahlen oder auf der visuellen Analogskala (VAS) gemessen [3-6]. Bei mehr als 5000 Messungen mit validierten Fragebogen in unserer Klinik hatten wir den Eindruck gewonnen, dass die VAS unbeliebt ist. Die Zusammenfassung ! Ziel: Die visuelle Analogskala (VAS) und Likert-Skala (LS) sind weit verbreitet obwohl die Patienten Schwierigkeiten beim Ausfüllen haben und die Auswertung fehleranfällig sein kann. Die visuelle Kreisskala (VCS) ist eine Kombination der bestehenden Skalen mit einer grafischen Abstufung in der Absicht, das Verständnis und die Auswertbarkeit zu verbessern. Methode: Die drei Skalen wurden bei orthopädischen Patienten in der postoperativen Phase zur Schmerzmessung angewendet und verglichen. Am Ende wurden diese Skalen durch die Patienten zur Einfachheit, Verständnis und der Allgemeineindruck beurteilt. Resultate: Eingeschlossen wurden 65 Patienten (40 Frauen) mit einem Durchschnittsalter von 66 Jahren mit 330 Schmerzmessungen und 65 Beurteilungen der Fragebogen. Die durchschnittliche Schmerzstärke war LS 42,7, VAS 39,3, VCS 44. Die Korrelationskoeffizienten r (Spearman) für alle Skalen untereinander waren > 0,89, ebenfalls für die Veränderung der Schmerzstärke. Die Patientenbeurteilung zeigte bei mehr als der Hälfte der Patienten eine Bevorzugung der VCS zur Messung von Schmerzen. Schlussfolgerung: Mit der VCS können die Schmerzen vergleichbar mit der VAS und Likert-Skala gemessen werden. Aus Sicht der Patienten wird die VCS gegenüber den anderen Skalen bevorzugt.

Methodology And Computing In Applied Probability

Let Xt, t[0Y 1, be a Gaussian process with continuous paths with mean zero and nonconstant varian... more Let Xt, t[0Y 1, be a Gaussian process with continuous paths with mean zero and nonconstant variance. The largest values of the Gaussian process occur in the neighborhood of the points of maximum variance. If there is a unique ®xed point t 0 in the interval 0Y 1, the behavior of Pfsup t[0Y1 Xt4ug is known for u??. We investigate the case where the unique point t 0 t u depends on u and tends to the boundary. This is reasonable for a family of Gaussian processes X u t depending on u, which have for each u such a unique point t u tending to the boundary as u??. We derive the asymptotic behavior of Pfsup t [ 0Y1 Xt4ug, depending on the rate as t u tends to 0 or 1. Some applications are mentioned and the computation of a particular case is used to compare simulated probabilities with the asymptotic formula. We consider the exceedances of such a nonconstant boundary by a Ornstein-Uhlenbeck process. It shows the dif®culties to simulate such rare events, when u is large.

Statistical Data Analysis and Inference, 1989

Testing the symmetry of an underlying distribution can be based on the empirical characterstic fu... more Testing the symmetry of an underlying distribution can be based on the empirical characterstic function. A crucial role of such tests is played by the first zero of the empirical characteristic function. We discuss in this paper the behaviour of such zeros depending on the underlying distribution function. In some cases, the first zero of the empirical characteristic function is related to the extreme value or extreme crossing events of a nonstationary Gaussian process. Recent results on such extreme values are used to derive the weak limit laws of the first zeros.

Extreme Value Theory and Applications, 1994

We review the limiting behaviour of extremes and exceedances of univariate and multivariate nonst... more We review the limiting behaviour of extremes and exceedances of univariate and multivariate nonstationary random sequences. The approach we present is based on an extension of the methods in the stationary case. It is extended also for any visits of the random sequence to some rare set, instead of the usual set (u n , ∞). We discuss some special cases as normal, periodic and independent sequences and review also the dependence structure of the components of the multivariate maxima.

Statistical Analysis of Extreme Values, 1997

We analyze the maximal daily temperature of the last 100 years at Prague. The aim of the study is... more We analyze the maximal daily temperature of the last 100 years at Prague. The aim of the study is to analyze whether the extreme values of the time series show an increase which reflects the global warming during the last 100 years. We are using the maximal yearly temperatures as well as the clustering of extreme temperatures for this analysis.

Laws of Small Numbers: Extremes and Rare Events, 2004

This chapter is based on the Pickands representation of multivariate extreme value dfs (EVDs) G, ... more This chapter is based on the Pickands representation of multivariate extreme value dfs (EVDs) G, see Section 4.3. Corresponding to the univariate case, we introduce certain multivariate, generalized Pareto dfs (GPDs) of the form W = 1+log(G) for the statistical modelling of multivariate exceedances, see Section 5.1, and deduce results for dfs which belong to the δ-neighborhood of multivariate GPDs, see Section 5.3.

Laws of Small Numbers: Extremes and Rare Events, 2010

We develop the general theory of extremes and exceedances of high boundaries by non-stationary ra... more We develop the general theory of extremes and exceedances of high boundaries by non-stationary random sequences. Of main interest is the asymptotic convergence of the point processes of exceedances or of clusters of exceedances. These results are then applied for special cases, as stationary, independent and particular nonstationary random sequences.

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1981

Let t~=max{k>O:Xk>flk } if such a k exists and =0 else, be the last exit time of the sequence X k... more Let t~=max{k>O:Xk>flk } if such a k exists and =0 else, be the last exit time of the sequence X k of independent, identically distributed random variables with EX~ < oe, fi > 0. We will prove sufficient conditions such that the law of the iterated logarithm holds for ta as fi~0. In discussing the relationships to the maximum Z,=max{X~,i<=n} we give weaker conditions for the law of the iterated logarithm of Z,(n-,oe) than the known conditions.

Stochastic Processes and their Applications, 1995

We consider general nonstationary max-autoregressive sequences {Xi, i>~ 1}, with X i = Z i max (X... more We consider general nonstationary max-autoregressive sequences {Xi, i>~ 1}, with X i = Z i max (Xi-1, Y3 where { Yi, i >~ 1 } is a sequence of i.i.d, random variables and {Zi, i >1 1 } is a sequence of independent random variables (0 ~< Z~ ~< 1), independent of { Y~}. We deal with the limit law of extreme values M. = max{X~, i~< n} (as n ~ oo) and evaluate the extremal index for the case where the marginal distribution of Y~ is regularly varying at oo. The limit of the point process of exceedances of a boundary u. by X i, i <~ n, is derived (as n ~ ~) by analysing the convergence of the cluster distribution and of the intensity measure.