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崔恒建教授学术报告

  发布日期:2016-10-27  浏览量:513


报告题目: Test of Significance on High Dimensional Covariance Matrix Structures

: 崔恒建 (首都师范大学教授、博士生导师、国家自然科学基金杰青(B)获得者)

报告时间: 201611 5(周六)上午10:30-11:30

报告地点: 磬苑校区澳门赌搏网站大全H306

报告摘要:This talk is concerned with test of significance on high dimensional covariance structures. In the classical multivariate analysis, the likelihood ratio tests have been derived for testing various covariance structures including test of sphericity and test of independence under a multinormality assumption. In this paper, our primary interest is to study the asymptotic behaviors of such likelihood ratio tests under the setting in which the limit of the ratio of the dimension of data to the sample size lies between 0 and 1. Using the modern random matrix theory, we derive the limiting null distributions of the likelihood ratio tests without multinormality assumption. Our theoretical analysis indicates that the likelihood ratio tests diverges to infinity as the sample size increases, and therefore the traditional likelihood ratio theory becomes invalid. We further conduct Monte Carlo simulation study on the likelihood ratio tests. Our simulation results show that the limiting null distribution provides quite accurate approximation to the null distribution so that the critical values taken from the limiting null distribution keeps the Type I error rate very well. Our simulation results clearly show that using the critical values from the corresponding chi-square distributions, the traditional limiting null distribution of the likelihood ratio tests, cannot preserve Type I error rate. Indeed the Type I error rate with the traditional critical values may be close to one under some settings. We further examine the power of the likelihood ratio tests using the newly derived null distribution. The simulation results show that the likelihood ratio tests are still very powerful with the new limiting null distribution. A real data example is used to illustrate the likelihood ratio tests.

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专家概况: 崔恒建,现为首都师范大学教授,博士生导师,曾任国务院学位委员会学科评议组专家。1983年毕业于北京师范大学数学系,1993年毕业于中国科学院系统科学研究所并获博士学位。1999年至2011年任北京师范大学数学系教授、博士生导师。崔恒建教授在数理统计和稳健统计理论和方法、金融统计、遥感统计与质量管理等领域取得过许多杰出的研究成果,发表论文100余篇,其中国内外核心刊物90余篇,包括发表在国际顶级的统计和计量经济学杂志《Annals of Statistics》、《Journal of Econometrics》、《Journal of the Royal Statistical Society》和《Biometrika》上,SCI索引的论文50余篇。多次赴美国、意大利、新加坡、澳大利亚和香港等著名大学进行学术合作研究。主持了国家自然科学基金杰青(B)项目和4项国家自然科学基金面上项目以及青年基金项目;主要参加了国家自然科学基金重点项目、主任基金项目、面上项目,教育部重大科研基金项目,科技部863项目,教育部留学回国人员基金,高校博士点专项基金等15余项。现担任《应用数学学报》中、英文版编委,《数理统计与管理》编委,中国现场统计学会常务理事,生存分析分会理事,国际泛华统计协会会员,美国数学会数学评论员,国际数理统计学会(中国分会)常务理事。曾获得教育部高等学校科学技术奖-自然科学奖二等奖;全国统计科学研究优秀成果奖一等奖;京津地区五四青年概率统计“盖洛普”奖;第六届中国科协期刊优秀学术论文奖等。

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