Multivariate tail coefficients are of interest when one is trying to summarize dependence of extremes. The difficulty is that these coefficients are defined as limits and thus to estimate them from ...data one needs to choose a kind of smoothing parameter kn. A standard approach in such problems is to choose the smoothing parameter as a minimum of an estimated asymptotic mean squared error (AMSE). In this paper several ways of estimating AMSE are suggested and investigated. We focus on estimating (Frahm’s) extremal dependence coefficient. In order to derive AMSE of this estimator we provide its asymptotic representation. Two methods (fully or partially nonparametric) of estimating AMSE are suggested. An extensive simulation study shows that both suggested methods usually slightly outperform the available alternatives with the fully nonparametric method being recommended. Finally the different ways of choosing kn are illustrated on a real data set.
•Multivariate tail coefficients summarize the dependence of extremes.•To calculate these coefficients in practice a choice of kn (a smoothing parameter) is required.•Existing choices of the smoothing parameter are reviewed and new ones are suggested.•The numerical performances of the different choices of the smoothing parameter are compared.
In this paper the interest is to elaborate on the generalization of bivariate association measures, namely Spearman’s rho, Kendall’s tau, Blomqvist’s beta and Gini’s gamma, for a general dimension ...d≥2. Desirable properties and axioms for such generalizations are discussed, where special attention is given to the impact of the addition of: (i) an independent random variable to a random vector; (ii) a conical combination of all components; (iii) a set of arbitrary random components. Existing generalizations are evaluated with respect to the axiom set. For a d-variate Gini’s gamma, a simplified formula is developed, making its analytical computation easier. Further, for Archimedean and meta-elliptical copulas the asymptotic behaviour when the dimension d increases is studied. Nonparametric estimation of the considered generalizations of multivariate association measures is reviewed and a nonparametric estimator of the multivariate Gini’s gamma is introduced. The practical use of multivariate association measures is illustrated on a real data example.
Multivariate tail coefficients are an important tool when investigating dependencies between extreme events for different components of a random vector. Although bivariate tail coefficients are ...well-studied, this is, to a lesser extent, the case for multivariate tail coefficients. This paper contributes to this research area by (i) providing a thorough study of properties of existing multivariate tail coefficients in the light of a set of desirable properties; (ii) proposing some new multivariate tail measurements; (iii) dealing with estimation of the discussed coefficients and establishing asymptotic consistency; and, (iv) studying the behavior of tail measurements with increasing dimension of the random vector. A set of illustrative examples is given, and practical use of the tail measurements is demonstrated in a data analysis with a focus on dependencies between stocks that are part of the EURO STOXX 50 market index.
Extrapulmonary tuberculosis (EPTB) in children globally represents a proportion of all cases of tuberculosis, reaching 20% according to published reports. Children are at a higher risk for ...disseminated TB and extrapulmonary forms. The most prevalent clinical presentations of EPTB in children worldwide are peripheral lymphadenitis and osteoarticular TB. Peritoneal, urogenital, or meningeal tuberculosis is less frequent, and their diagnosis is often difficult. The aim of the study was the determination of EPTB incidence in children in a low-prevalence region over 35 years.
Descriptive retrospective study of the incidence of EPTB in children and adolescents (aged 0-18 years) in the Czech Republic in the years 1987-2021 as reported in the tuberculosis register.
Total amount of EPTB cases was 95. The most prevalent form was extrathoracic lymph node TB. The median age was 10 years. Most patients (84%) were Czechs. None of them died. The ratio of pulmonary and extrapulmonary TB was 79.8% to 20.2%.
The low incidence of EPTB in Czech children is congruent with a low incidence of TB in the Czech Republic. Our study confirms that the most frequent form of EPTB is peripheral lymph node TB. Our study did not prove a significant change in the trend of EPTB after the cessation of the mandatory Bacillus Calmette-Guerin (BCG) vaccination programme.
Diploma thesis abstract Thesis title: Statistical inference in multivariate distributions based on copula models Author: Vojtěch Kika This diploma thesis aims for statistical inference in copula ...based models. Ba- sics of copula theory are described, followed by methods for statistical inference. These are divided into three main groups. First of them are parametric methods for copula parameter estimation which assume fully parametric structure, thus for both joint and marginal distributions. The second group consists of semi- parametric methods for copula parameter estimation which, unlike parametric methods, do not require parametric structure for marginal distributions. The last group describes goodness-of-fit tests used for testing the hypothesis that consi- dered copula belongs to some specific copula family. The thesis is accompanied by a simulation study that investigates the dependence of the observed coverage of the asymptotic confidence intervals for copula parameter on the sample size. Pseudolikelihood method was chosen for the simulation study since it is one of the most popular semiparametric methods. It is shown that sample size of 50 seems to be sufficient for the observed coverage to be close to the theoretical one. For Frank and Gumbel-Hougaard copula families even sample size of 30 gives us...
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