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摘要翻译：
给出了一类无穷方差稳定随机变量函数的协方差界，包括幂函数和对数等无界函数。这些界限涉及稳定变量之间的相关性度量，其中一些是新的。本文还利用这些界导出了稳定滑动平均时间序列无界函数的中心极限定理。这一结果推广了Tailen Hsing和作者关于稳定移动平均有界函数的中心极限定理的早期结果。它可以用来表示分数阶稳定运动中自相似参数的小波估计的渐近正态性。
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英文标题：
《Bounds for the covariance of functions of infinite variance stable
random variables with applications to central limit theorems and
wavelet-based estimation》
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作者：
Vladas Pipiras, Murad S. Taqqu, Patrice Abry
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence between the stable variables, some of which are new. The bounds are also used to deduce the central limit theorem for unbounded functions of stable moving average time series. This result extends the earlier results of Tailen Hsing and the authors on central limit theorems for bounded functions of stable moving averages. It can be used to show asymptotic normality of wavelet-based estimators of the self-similarity parameter in fractional stable motions.
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PDF链接：
https://arxiv.org/pdf/711.4457
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