Elliptically Contoured Distribution (original) (raw)
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The problem of estimation of the scale matrix of a class of elliptical distributions is considered. We propose an improved class of estimators for scale matrix. The exact forms of the risk functions are derived as well. The relative merits of the class of improved estimators to the usual one are appraised in the light of a quadratic loss function. The conditions under which the class of proposed estimators outperform the class of usual estimators are obtained. Relative Risk is also computed for a special case. Some important characteristics of scale matrix are also considered for estimation.
Estimation of the scale matrix of a class of elliptical distributions
Metrika, 1998
The problem of estimation of the scale matrix of a class of elliptical distributions is considered. We propose an improved class of estimators for scale matrix. The exact forms of the risk functions are derived as well. The relative merits of the class of improved estimators to the usual one are appraised in the light of a quadratic loss function. The conditions under which the class of proposed estimators outperform the class of usual estimators are obtained. Relative Risk is also computed for a special case. Some important characteristics of scale matrix are also considered for estimation.
A multivariate tail covariance measure for elliptical distributions
Insurance: Mathematics and Economics, 2018
This paper introduces a multivariate tail covariance (MTCov) measure, which is a matrix-valued risk measure designed to explore the tail dispersion of multivariate loss distributions. The MTCov is the second multivariate tail conditional moment around the MTCE, the multivariate tail conditional expectation (MTCE) risk measure. Although MTCE was recently introduced in (Landsman et al., 2016), in this paper we essentially generalize it, allowing for quantile levels to obtain the different values corresponded to each risk. The MTCov measure, which is also defined for the set of different quantile levels, allows us to investigate more deeply the tail of multivariate distributions, since it focuses on the variance-covariance dependence structure of a system of dependent risks. As a natural extension, we also introduced the multivariate tail correlation matrix (MTCorr). The properties of this risk measure are explored and its explicit closed-form expression is derived for the elliptical family of distributions. As a special case, we consider the normal, Student-t and Laplace distributions, prevalent in actuarial science and finance. The results are illustrated numerically with data of some stock returns.
The estimation of the eigenvalues of the scale matrix of a class of elliptical distributions is considered. The multivariate normal distribution and the multivariate l-distribution are the two important special cases of the class of elliptical distributions. This class of distributions contains thin tailed as well as fat talled distributions and hence is important in modeling many real world data. Many authors have observed that empirical distributions of the rates of return of common stocks have relatively fatter tails than those of the normal distribution. Zellner (191 6) has considered a regression model with errors having a multivaiate t-distribution to study stock market data for a single stock.
The estimation of the eigenvalues of the scale matrix of a class of elliptical distributions is considered. The multivariate normal distribution and the multivariate l-distribution are the two important special cases of the class of elliptical distributions. This class of distributions contains thin tailed as well as fat talled distributions and hence is important in modeling many real world data. Many authors have observed that empirical distributions of the rates of return of common stocks have relatively fatter tails than those of the normal distribution. Zellner (191 6) has considered a regression model with errors having a multivaiate t-distribution to study stock market data for a single stock.
Multivariate elliptically contoured stable distributions: theory and estimation
Computational Statistics, 2013
Mulitvariate stable distributions with elliptical contours are a class of heavy tailed distributions that can be useful for modeling financial data. This paper describes the theory of such distributions, presents formulas for calculating their densities, methods for fitting the data and assessing the fit. Numerical routines are described that work for dimension d ≤ 40. An example looks at a portfolio with 30 assets.