论文标题
基于订单统计比率的定期变化指数的分布敏感估计器
Distribution sensitive estimators of the index of regular variation based on ratios of order statistics
论文作者
论文摘要
中央顺序统计数据的比率似乎对于估计分布的尾巴以及数据范围以外的分位数非常有用。在1995年，伊莎贝尔·弗拉格（Isabel Fraga Alves）研究了尾部指数参数的三个半参数估计量的收敛速率，以防观察到的随机变量的累积分布函数属于固定概括性极值分布的最大域。它们基于两个极端阶统计的特定线性变换的比率。在2019年，我们考虑了帕累托病例，发现了两个常规变化索引的非常简单且无偏的估计量。然后，使用中央顺序统计数据，我们表明这些估计器具有许多良好的属性。然后，我们观察到，尽管假设是不同的，但其中一个等同于Alves的估计器之一。使用中央顺序统计，我们证明了无偏见，渐近一致性，渐近正态性和渐近效率。在这里，我们再次使用中央顺序统计和参数方法，并在某些特定情况下获得常规变化索引的分布敏感估计器。然后，我们发现可以保证这些估计器公正，一致和渐近正常的条件。结果通过仿真研究描述。
Ratios of central order statistics seem to be very useful for estimating the tail of the distributions and therefore, quantiles outside the range of the data. In 1995 Isabel Fraga Alves investigated the rate of convergence of three semi-parametric estimators of the parameter of the tail index in case when the cumulative distribution function of the observed random variable belongs to the max-domain of attraction of a fixed Generalized Extreme Value Distribution. They are based on ratios of specific linear transformations of two extreme order statistics. In 2019 we considered Pareto case and found two very simple and unbiased estimators of the index of regular variation. Then, using the central order statistics we showed that these estimators have many good properties. Then, we observed that although the assumptions are different, one of them is equivalent to one of Alves's estimators. Using central order statistics we proved unbiasedness, asymptotic consistency, asymptotic normality and asymptotic efficiency. Here we use again central order statistics and a parametric approach and obtain distribution sensitive estimators of the index of regular variation in some particular cases. Then, we find conditions which guarantee that these estimators are unbiased, consistent and asymptotically normal. The results are depicted via simulation study.
