Tail index estimation, concentration and adaptivity
نویسندگان
چکیده
منابع مشابه
Tail index estimation, concentration and adaptivity
This paper presents an adaptive version of the Hill estimator based on Lespki’s model selection method. This simple data-driven index selection method is shown to satisfy an oracle inequality and is checked to achieve the lower bound recently derived by Carpentier and Kim. In order to establish the oracle inequality, we derive non-asymptotic variance bounds and concentration inequalities for Hi...
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• The estimation of the extreme-value index γ based on a sample of independent and identically distributed random variables has received considerable attention in the extreme-value literature. However, the problem of combining data from several groups is hardly studied. In this paper we discuss the simultaneous estimation of tail indices when data on several independent data groups are availabl...
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Both parametric distribution functions appearing in extreme value theory the generalized extreme value distribution and the generalized Pareto distribution have log-concave densities if the extreme value index γ ∈ [−1, 0]. Replacing the order statistics in tail index estimators by their corresponding quantiles from the distribution function that is based on the estimated log-concave density f̂n ...
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A general method of tail index estimation for heavy-tailed time series, based on examining the growth rate of the logged sample second moment of the data was proposed and studied in Meerschaert and Scheffler (1998) as well as Politis (2002). To improve upon the basic estimator, we introduce a scale-invariant estimator that is computed over subsets of the whole data set. We show that the new est...
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Problem 1. Use Markov inequality to prove the following. Let c ≥ 1 be an arbitrary constant. If n people have a total of d dollars, then there are at least (1− 1/c)n of them each of whom has less than cd/n dollars. (You can easily prove the above statement from first principle. However, please set up a probability space, a random variable, and use Markov inequality to prove it. It is instructive!)
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ژورنال
عنوان ژورنال: Electronic Journal of Statistics
سال: 2015
ISSN: 1935-7524
DOI: 10.1214/15-ejs1088