A semi-parametric estimation of copula models based on moments method under right censoring

Based on the classical estimation method of moments, a new copula estimator was proposed for censored bivariate data. As theoretical results, general formulas were proved with analytical forms of the obtained estimators. Taking into account Lopez and Saint-Pierre’s(2012)[19], Gribkova and Lopez’s (2015)[10] results, the asymptotic normality of the empirical survival copula was established. The dependence structure between the bivariate survival times was modeled under the assumption that the underlying copula is Archimedean. Accounting for various censoring patterns (singly or doubly censored), a simulation study was performed enlighten the behavior of the procedure estimation method, shown the efficiency and robustness of the new estimator proposed.Publisher's Versio

Modified bisection algorithm in estimating the extreme value index under random censoring

The Generalized Pareto Distribution (GPD) has long been employed in the theories of extreme values. In this paper, we are interested by estimating the extreme value index under censoring. Using a maximum likelihood estimator (MLE) and a numerical method algorithm, a new approach is proposed to estimate the extreme value index by maximizing the adaptive log-likelihood of GPD given censored data. We also show how to construct the maximum likelihood estimate of the GPD parameters (shape and scale) using censored data. Lastly, numerical examples are provided at the end of the paper to show the method’s reliability and to better illustrate the findings of this research.Publisher's Versio

Bivariate copulas parameters estimation using the trimmed L-moments method

The main purpose of this paper is to use the trimmed L-moments method for the introduction of a new estimator of multi-parametric copulas in the case where the mean does not exist. The consistency and asymptotic normality of this estimator is established. An extended simulation study shows the performance of the new estimator is carried.Keywords: Copulas; Dependence; Bivariate L-moments; Trimmed L-moments; Trimmed L-comoment

Copula conditional tail expectation for multivariate financial risks

Our goal in this paper is to propose an alternative risk measure which takes into account the fluctuations of losses and possible correlations between random variables. This new notion of risk measures, that we call Copula Conditional Tail Expectation describes the expected amount of risk that can be experienced given that a potential bivariate risk exceeds a bivariate threshold value, and provides an important measure for right-tail risk. An application to real financial data is given

Nonparametric estimation of the copula function with bivariate twice censored data

In this work, we are interested in the nonparametric estimation of the copula function in the presence of bivariate twice censored data. Assuming that the copula functions of the right and the left censoring variables are known, we propose an estimator of the joint distribution function of the variables of interest, then we derive an estimator of their copula function. Using a representation of the proposed estimator of the joint distribution function as a sum of independent and identically distributed variables, we establish the weak convergence of the empirical copula that we introduce

Оценка индекса тяжелого хвоста с помощью взвешенной ранговой регрессии по методу наименьших квадратов

In this paper, we proposed a weighted least square estimator based method to estimate the shape parameter of the Frechet distribution. We show the performance of the proposed estimator in a simulation study, it is found that the considered weighted estimation method shows better performance than the maximum likelihood estimation. Maximum product of spacing estimation and least-squares in terms of bias and root mean square error for most of the considered sample sizes. In addition, a real example from Danish data is provided to demonstrate the performance of the considered methodВ этой статье мы предложили метод взвешенной оценки методом наименьших квадратов для оценки параметра формы распределения Фреше. Мы показываем производительность предложенной оценки в имитационном исследовании, установлено, что рассматриваемый метод взвешенной оценки показывает лучшую производительность, чем оценка максимального правдоподобия. Максимальное произведение оценки интервала и метода наименьших квадратов с точки зрения систематической ошибки и среднеквадратичной ошибки для большинства рассматриваемых размеров выборки. Кроме того, приведен реальный пример из датских данных, демонстрирующий работоспособность рассматриваемого метод