| 独立非同分布二元高斯三角阵最大值的渐近性及相关统计推断 |
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| 引用本文： | 廖昕,彭作祥.独立非同分布二元高斯三角阵最大值的渐近性及相关统计推断[J].数学学报,2017,60(2):297-314. |
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| 作者姓名： | 廖昕 彭作祥 |
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| 作者单位： | 1. 上海理工大学管理学院 上海 200093;
2. 西南大学数学与统计学院 重庆 400715 |
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| 基金项目： | 国家自然科学基金资助项目（11171275）；重庆市自然科学基金资助项目（cstc2012jjA00029）；上海理工大学博士启动项目（BSQD201608） |
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| 摘 要： | 考虑二元独立非同分布高斯随机向量三角阵列最大值分布的渐近性及相关统计推断.此高斯三角阵的第n列的第i个向量服从二元高斯分布,其相关系数为i/n的函数并单调连续.首先建立了此高斯三角阵最大值分布的一阶和二阶渐近展开式.其次,分析相关系数参数估计及估计量的渐近性质.最后,通过随机模拟说明了相关系数之参数估计的有效性,并将该二元非同分布三角阵列模型应用于实际数据,得到了满意的结果.
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| 关 键 词： | 二元高斯随机向量 最大值 极限分布 二阶渐近展开 参数估计 |
Asymptotics and Statistical Inferences on Independent and Non-identically Distributed Bivariate Gaussian Triangular Arrays |
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| Xin LIAO,Zuo Xiang PENG.Asymptotics and Statistical Inferences on Independent and Non-identically Distributed Bivariate Gaussian Triangular Arrays[J].Acta Mathematica Sinica,2017,60(2):297-314. |
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| Authors: | Xin LIAO Zuo Xiang PENG |
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| Institution: | 1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;
2. School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China |
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| Abstract: | We establish the first and the second-order asymptotics of distributions of normalized maxima of independent and non-identically distributed bivariate Gaussian triangular arrays, where each vector of the n-th row follows from a bivariate Gaussian distribution with correlation coefficient being a monotone continuous positive function of i/n. Furthermore, parametric inference for this unknown function is studied. Some simulation study and real data sets analysis are also presented. |
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| Keywords: | bivariate gaussian random vector maximum limiting distribution secondorder expansion parameter estimation |
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