Likelihood estimation of the extremal index

The article develops the approach of Ferro and Segers (J.R. Stat. Soc., Ser. B 65:545, 2003) to the estimation of the extremal index, and proposes the use of a new variable decreasing the bias of the likelihood based on the point process character of the exceedances. Two estimators are discussed: a maximum likelihood estimator and an iterative least squares estimator based on the normalized gaps between clusters. The first provides a flexible tool for use with smoothing methods. A diagnostic is given for condition $D^{(2)}(u_n)$ , under which maximum likelihood is valid. The performance of the new estimators were tested by extensive simulations. An application to the Central England temperature series demonstrates the use of the maximum likelihood estimator together with smoothing method

Model misspecification in peaks over threshold analysis

Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows the estimation of the marginal distribution of threshold exceedances and of the mean cluster size, but requires the choice of a threshold and of a run parameter, $K$, that determines how exceedances are declustered. We extend a class of estimators of the reciprocal mean cluster size, known as the extremal index, establish consistency and asymptotic normality, and use the compound Poisson process to derive misspecification tests of model validity and of the choice of run parameter and threshold. Simulated examples and real data on temperatures and rainfall illustrate the ideas, both for estimating the extremal index in nonstandard situations and for assessing the validity of extremal models.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS292 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Pathological and immunological study of an in ovo complex vaccine against infectious bursal disease

The appearance of very virulent strains of infectious bursal disease (IBD) virus at the end of the 1980s made it necessary to develop more effective immunization procedures. To facilitate this, the immunogenicity and the immunosuppressive effect of a mild (G-87), an intermediate (LIBD) and an intermediate-plus (IBDV 2512) IBDV strain were tested after the in ovo inoculation of 18-day-old SPF and broiler chicken embryos. It was established that no noteworthy difference existed between the immunized and the control embryos in hatching rate and hatching weight. The higher the virulence of the vaccine virus strain, the more severe damage it caused to the lymphocytes of the bursa of Fabricius. In SPF chickens, the haemagglutination inhibition (HI) titres induced by a Newcastle disease (ND) vaccine administered at day old decreased in inverse ratio to the virulence of the IBD vaccine strain, while in broiler chickens this was not observed. Despite the decrease of the HI titre, the level of protection did not decline, or did so only after the use of the ‘hot’ strain. SPF chickens immunized in ovo with a complex vaccine prepared from strain IBDV 2512 and IBD antibody showed the same protection against Newcastle disease as the broilers. In broiler chicken embryos immunized in ovo, only strain IBDV 2512 induced antibody production, and such chickens were protected against IBD at 3 weeks of age. The complex vaccine administered in ovo has been used successfully at farm hatcheries as well

Statistical analysis of clusters of extreme events

The thesis is a contribution to extreme-value statistics, more precisely to the estimation of clustering characteristics of extreme values. One summary measure of the tendency to form groups is the inverse average cluster size. In extreme-value context, this parameter is called the extremal index, and apart from its relation with the size of groups, it appears as an important parameter measuring the effects of serial dependence on extreme levels in time series. Although several methods exist for its estimation in univariate sequences, these methods are only applicable for strictly stationary series satisfying a long-range asymptotic independence condition on extreme levels, cannot take covariates into consideration, and yield only crude estimates for the corresponding multivariate quantity. These are strong restrictions and great drawbacks. In climatic time series, both stationarity and asymptotic independence can be broken, due to climate change and possible long memory of the data, and not including information from simultaneously measured linked variables may lead to inefficient estimation. The thesis addresses these issues. First, we extend the theorem of Ferro and Segers (2003) concerning the distribution of inter-exceedance times: we introduce truncated inter-exceedance times, called K-gaps, and show that they follow the same exponential-point mass mixture distribution as the inter-exceedance times. The maximization of the likelihood built on this distribution yields a simple closed-form estimator for the extremal index. The method can admit covariates and can be applied with smoothing techniques, which allows its use in a nonstationary setting. Simulated and real data examples demonstrate the smooth estimation of the extremal index. The likelihood, based on an assumption of independence of the K-gaps, is misspecified whenever K is too small. This motivates another contribution of the thesis, the introduction into extreme-value statistics of misspecification tests based on the information matrix. For our likelihood, they are able to detect misspecification from any source, not only those due to a bad choice of the truncation parameter. They provide help also in threshold selection, and show whether the fundamental assumptions of stationarity or asymptotic independence are broken. Moreover, these diagnostic tests are of general use, and could be adapted to many kinds of extreme-value models, which are always approximate. Simulated examples demonstrate the performance of the misspecification tests in the context of extremal index estimation. Two data examples with complex behaviour, one univariate and the other bivariate, offer insight into their power in discovering situations where the fundamental assumptions of the likelihood model are not valid. In the multivariate case, the parameter corresponding to the univariate extremal index is the multivariate extremal index function. As in the univariate case, its appearance is linked to serial dependence in the observed processes. Univariate estimation methods can be applied, but are likely to give crude, unreasonably varying, estimates, and the constraints on the extremal index function implied by the characteristics of the stable tail dependence function are not automatically satisfied. The third contribution of the thesis is the development of methodology based on the M4 approximation of Smith and Weissman (1996), which can be used to estimate the multivariate extremal index, as well as other cluster characteristics. For this purpose, we give a preliminary cluster selection procedure, and approximate the noise on finite levels with a flexible semiparametric model, the Dirichlet mixtures used widely in Bayesian analysis. The model is fitted by the EM algorithm. Advantages and drawbacks of the method are discussed using the same univariate and bivariate examples as the likelihood methods

Competence examination of finance and accounting students - Students' point of view

The purpose of the research is to identify the competencies required of students and to explore the missing competencies in order to improve the content and methodology of financial and accounting training in higher education. In order to fulfill our research goals we examined these surveys and other research reports during our secondary research. After our secondary research we formulated statements about our educational development, which we examined in the second part of the research during our primary research. In the first part of this study, we present the trends that make the competence-based education more and more widespread, and the factors that generate methodological changes in the transfer of knowledge in financial and accounting courses. In the second part, we present the results of our questionnaire research, which contains the students’ opinions

Analysis of GJB2 mutations and the clinical manifestation in a large Hungarian cohort

Pathogenic variants of the gap junction beta 2 (GJB2) gene are responsible for about 50% of hereditary non-syndromic sensorineural hearing loss (NSHL). In this study, we report mutation frequency and phenotype comparison of different GJB2 gene alterations in Hungarian NSHL patients