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宾州州立大学 李润泽教授: Hypothesis Testing on Linear Structures of High Dimensional Covariance Matrix

([西财新闻] 发布于 :2019-07-03 )

光華講壇——社會名流與企業家論壇第5480期

 

主題:Hypothesis Testing on Linear Structures of High Dimensional Covariance Matrix

主講人:宾州州立大学 李润泽教授

主持人:周岭 副教授

時間:2019年7月5日(星期) 下午14:00-15:00

地點:人人棋牌柳林校区弘远楼408会议室

主辦單位:统计研究中心 统计学院 科研处

 

主講人簡介:

李润泽是宾州州立大学讲席教授。他的研究方向包括高维数据建模,非参数回归,半参数回归及其统计学的应用。他是IMS,ASA和AAAS fellow。他曾担任Annals of Statistics的副主编、主编。现担任Journal of American Statistical Association的副主编。

主要內容:

This paper is concerned with test of significance on high dimensional covariance structures, and aims to develop a unified framework for testing commonly-used linear covariance structures. We first construct a consistent estimator for parameters involved in the linear covariance structure, and then develop two tests for the linear covariance structures based on entropy loss and quadratic loss used for covariance matrix estimation. To study the asymptotic properties of the proposed tests, we study related high dimensional random matrix theory, and establish several highly useful asymptotic results. With the aid of these asymptotic results, we derive the limiting distributions of these two tests under the null and alternative hypotheses. We further show that the quadratic loss based test is asymptotically unbiased. We conduct Monte Carlo simulation study to examine the finite sample performance of the two tests. Our simulation results show that the limiting null distributions approximate their null distributions quite well, and the corresponding asymptotic critical values keep Type I error rate very well. Our numerical comparison implies that the proposed tests outperform existing ones in terms of controlling Type I error rate and power. Our simulation indicates that the test based on quadratic loss seems to have better power than the test based on entropy loss.

本文關注高維協方差結構的重要性測試,旨在開發一個統一的測試常用線性協方差結構的框架。我們首先構造線性協方差結構中涉及的參數的一致估計,然後基于用于協方差矩陣估計的熵損失和二次損失開發線性協方差結構的兩個測試。爲了研究所提出的測試的漸近性質,我們研究了相關的高維隨機矩陣理論,並建立了幾個非常有用的漸近結果。借助于這些漸近結果,我們在無效和替代假設下推導出這兩個測試的極限分布。我們進一步表明,基于二次損失的測試是漸近無偏的。我們進行蒙特卡羅模擬研究,以檢驗兩個測試的有限樣本性能。我們的仿真結果表明,極限零分布非常接近它們的零分布,相應的漸近臨界值很好地保持了I類誤差率。我們的數值比較表明,在控制I類錯誤率和功率方面,所提出的測試優于現有測試。我們的模擬表明,基于二次損失的測試似乎比基于熵損失的測試具有更好的功效。

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