Wang Chen-Pin, Ghosh Malay
Department of Epidemiology and Biostatistics, University of Texas Health Science Center, San Antonio, USA.
Department of Statistics, University of Florida, Gainesville, USA.
Open J Stat. 2011 Oct;1(3):172-184. doi: 10.4236/ojs.2011.13021.
This paper considers a Kullback-Leibler distance (KLD) which is asymptotically equivalent to the KLD by Goutis and Robert [1] when the reference model (in comparison to a competing fitted model) is correctly specified and that certain regularity conditions hold true (ref. Akaike [2]). We derive the asymptotic property of this Goutis-Robert-Akaike KLD under certain regularity conditions. We also examine the impact of this asymptotic property when the regularity conditions are partially satisfied. Furthermore, the connection between the Goutis-Robert-Akaike KLD and a weighted posterior predictive p-value (WPPP) is established. Finally, both the Goutis-Robert-Akaike KLD and WPPP are applied to compare models using various simulated examples as well as two cohort studies of diabetes.
本文考虑了一种库尔贝克-莱布勒散度（KLD），当参考模型（与竞争拟合模型相比）被正确指定且某些正则性条件成立时（参考文献：赤池[2]），该散度与Goutis和Robert [1]提出的KLD渐近等价。我们在某些正则性条件下推导了这种Goutis-Robert-赤池KLD的渐近性质。我们还研究了正则性条件部分满足时这种渐近性质的影响。此外，建立了Goutis-Robert-赤池KLD与加权后验预测p值（WPPP）之间的联系。最后，将Goutis-Robert-赤池KLD和WPPP都应用于使用各种模拟示例以及两项糖尿病队列研究来比较模型。
