A robust estimator for the tail index of Pareto-type distributions
نویسندگان
چکیده
In extreme value statistics, the extreme value index is a well-known parameter to measure the tail heaviness of a distribution. Pareto-type distributions, with strictly positive extreme value index (or tail index) are considered. The most prominent extreme value methods are constructed on efficient maximum likelihood estimators based on specific parametric models which are fitted to excesses over large thresholds. Maximum likelihood estimators however are often not very robust, which makes them sensitive to few particular observations. Even in extreme value statistics, where the most extreme data usually receive most attention, this can constitute a serious problem. The problem is illustrated on a real data set from geopedology, in which a few abnormal soil measurements highly influence the estimates of the tail index. In order to overcome this problem, a robust estimator of the tail index is proposed, by combining a refinement of the Pareto approximation for the conditional distribution of relative excesses over a large threshold with an integrated squared error approach on partial density component estimation. It is shown that the influence function of this newly proposed estimator is bounded and through several simulations it is illustrated that it performs reasonably well at contaminated as well as uncontaminated data.
منابع مشابه
An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index
We introduce a robust and asymptotically unbiased estimator for the tail index of Pareto-type distributions. The estimator is obtained by fitting the extended Pareto distribution to the relative excesses over a high threshold with the minimum density power divergence criterion. Consistency and asymptotic normality of the estimator is established under a second order condition on the distributio...
متن کاملDivergence based robust estimation of the tail index through an exponential regression model
The extreme value theory is very popular in applied sciences including finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of attraction (MAD) characterized by its tail index; there are three broad classes of tails – the Pareto type, the Weibull type and the Gumbel type. The simple...
متن کاملDetecting influential data points for the Hill estimator in Pareto-type distributions
Pareto-type distributions are extreme value distributions for which the extreme value index γ > 0. Classical estimators for γ > 0, like the Hill estimator, tend to overestimate this parameter in the presence of outliers. The empirical influence function plot, which displays the influence that each data point has on the Hill estimator, is introduced. To avoid a masking effect, the empirical infl...
متن کاملRobust estimation of the Pareto index: A Monte Carlo Analysis
The Pareto distribution is often used in many areas of economics to model the right tail of heavytailed distributions. However, the standard method of estimating the shape parameter (the Pareto index) of this distribution– the maximum likelihood estimator (MLE) – is non-robust, in the sense that it is very sensitive to extreme observations, data contamination or model deviation. In recent years...
متن کاملEstimation of extreme quantiles from heavy and light tailed distributions
In [18], a new family of distributions is introduced, depending on two parameters τ and θ, which encompasses Pareto-type distributions as well as Weibull tail-distributions. Estimators for θ and extreme quantiles are also proposed, but they both depend on the unknown parameter τ , making them useless in practical situations. In this paper, we propose an estimator of τ which is independent of θ....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computational Statistics & Data Analysis
دوره 51 شماره
صفحات -
تاریخ انتشار 2007