一般协方差矩阵下的修正Akaike信息准则  

Corrected Akaike information criterion with general covariance matrix

作　　者：赵尚威[1] 喻达磊 张新雨[3] Shangwei Zhao;Dalei Yu;Xinyu Zhang

机构地区：[1]中央民族大学理学院,北京100081 [2]云南财经大学统计与数学学院,昆明650221 [3]中国科学院数学与系统科学研究院,北京100190

出　　处：《中国科学：数学》2022年第5期555-582,共28页Scientia Sinica：Mathematica

基　　金：国家重点研发计划(批准号:2020AAA0105200);国家自然科学基金(批准号:11661079,71925007和11688101);中国科学院青年创新促进会;北京智源人工智能研究院资助项目。

摘　　要：本文在Stein恒等式(Stein’s identity)的框架下,给出了一种适用于有限样本场合的全新的修正Akaike信息准则(corrected Akaike information criterion),所提出的新准则适用于非常一般的协方差结构.在一定的正则性条件下,本文建立了所提出准则的渐近有效性.应用带有自回归误差的空间回归模型进行模拟,结果表明,在备选模型与真实的数据生成过程之间的差异较小时,本文所提出方法的表现是令人满意的.当这种差异变大时,本文所提出的方法与其他已有方法相比也非常有竞争力.所提出的方法也被用于一组实际数据(社区犯罪数据)的分析中,所得到的结果更进一步支持了我们的方法在实际数据分析中的应用.In this paper, within the framework of Stein’s identity, we propose a new corrected Akaike information criterion for the finite sample setting. The new criterion applies to the situation where very general covariance structures are involved. Under certain regularity conditions, we establish the asymptotic efficiency of the proposed model selection criterion. Simulations in the spatial regression model with autoregressive errors show that our method is promising when the difference between the candidate models and the true data generating process is small. Our method becomes particularly competitive with its competitors when such difference becomes larger.The proposed model selection criterion is also applied to the analysis of a set of real data(the Neighborhood Crimes Data) and the results further support the use of our method in practical situations.

关 键 词：渐近有效性 修正Akaike信息准则 模型选择 空间自回归误差 

分 类 号：O212.1[理学—概率论与数理统计]