| 刘维奇,梁珊珊.一类新的位置不变矩估计及其渐近正态性[J].数学研究及应用,2018,38(3):293~302 |
| 一类新的位置不变矩估计及其渐近正态性 |
| A New Location Invariant Moment-Type Estimator and Its Asymptotic Normality |
| 投稿时间：2017-03-16 修订日期：2018-03-01 |
| DOI：10.3770/j.issn:2095-2651.2018.03.008 |
| 中文关键词: 极值指数 矩估计 正则变化 位置不变 渐近性质 |
| 英文关键词:extreme value index moment-type estimator regular variation location invariant asymptotic normality |
| 基金项目:国家自然科学基金(Grant No.15BJY164). |
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| 中文摘要: |
| 在极值理论中矩估计被广泛应用于估计极值指数,但它不满足位置不变性,文章基于矩估计提出了一类新的位置不变矩估计量,并在二阶正则变化条件下讨论了它的渐近正态性,最后模拟比较了新估计量和凌提出的另一个位置不变的矩估计量$\hat{\gamma}_{n}^{M}(k_{0},k)$,结果表明,新估计量有良好的性质. |
| 英文摘要: |
| The moment estimator has been widely used in extreme value theory in order to estimate the extreme value index, however it is not location invariant. In this paper, based on the moment-type estimator, we propose a new location invariant moment-type estimator, and discuss its asymptotic normality under the second order regular variation. Finally, a simulation is presented to compare this new estimator with another location invariant moment-type estimator $\hat{\gamma}_{n}^{M}(k_{0},k)$ proposed by Ling, which indicates that the new estimator has good performances. |
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