一般协方差矩阵下的修正Akaike信息准则

Corrected Akaike information criterion with general covariance matrix

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.