منابع مشابه
A Multivariate Hill Estimator
We propose a simple and semi-parametric estimator for the tail index of a regular varying elliptical random vector. Since, for univariate random variables, our estimator boils down to the Hill estimator and it inherits the simplicity and asymptotic properties, we name it after Bruce M. Hill. The estimator is based on the distance between an elliptical probability contour and the outer – or exce...
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The moment’s estimator (Dekkers et al., 1989) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The location invariant Hill-type estimator (Fraga Alves, 2001) is only suitable to estimate positive indices. In this paper, a new moment-type estimator is studied, which is location invariant. This new estimator is based on the original moment-type e...
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Consider the modelY = μ+ σ · E, μ ∈ R, σ ∈ R+,where E follows a known distribution F. The parameter μ is called the location parameter. Pit-man (1939) introduced a method to determine an optimal equivariant estimator of μ, when thedistribution F is continuous, but otherwise of any form. This method uses a conditioning on anancillary statistic to minimize the mean square ...
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متن کاملAsymptotic normality of Hill Estimator for truncated data
The problem of estimating the tail index from truncated data is addressed in ?. In that paper, a sample based (and hence random) choice of k is suggested, and it is shown that the choice leads to a consistent estimator of the inverse of the tail index. In this paper, the second order behavior of the Hill estimator with that choice of k is studied, under some additional assumptions. In the untru...
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ژورنال
عنوان ژورنال: Extremes
سال: 2011
ISSN: 1386-1999,1572-915X
DOI: 10.1007/s10687-011-0134-x