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- W1570479612 abstract "The following class of sum-product statistics T_n(p)=frac{1}{k}sum_{h=1}^p sum_{(s_1...s_h)in P(p,h)} sum_{i_1=l+1}^{i_0} ... sum_{i_h=l+1}^{i_{h-1}} i_h prod_{i=i_1}^{i_h} frac{(Y_{n-i+1,n}-Y_{n-i,n})^{s_i}}{s_i!} (where $l,$ $k=i_{0}$ and n are positive integers, $0 0$ into $ h$ positive integers and $Y_{1,n}leq ...leq Y_{n,n}$ are the order statistics based on a sequence of independent random variables $Y_{1},$ $Y_{2},...$with underlying distribution $mathbb{P}(Yleq y)=G(Y)=F(e^{y})$), is introduced. For each p, $T_{n}(p)^{-1/p}$ is an estimator of the index of a distribution whose upper tail varies regularly at infinity. This family generalizes the so called Hill statistic and the Dekkers-Einmahl-De Haan one. We study the limiting laws of the process ${T_{n}(p),1leq p<infty}$ and completely describe the covariance function of the Gaussian limiting process with the help of combinatorial techniques. Many results available for Hill's statistic regarding asymptotic normality and laws of the iterated logarithm are extended to each margin $T_{n}(p,k)$, for $p$ fixed, and for any distribution function lying in the extremal domain. In the process, we obtain special classes of numbers related to those of paths joining the opposite coins within a parallelogram." @default.
- W1570479612 created "2016-06-24" @default.
- W1570479612 creator A5000193182 @default.
- W1570479612 date "2012-03-03" @default.
- W1570479612 modified "2023-09-27" @default.
- W1570479612 title "On a discrete Hill's statistical process based on sum-product statistics and its finite-dimensional asymptotic theory" @default.
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