基于φ-散度的乘积多项抽样下对数线性模型的检验水平和功效(英文)  

Size and power considerations for testing loglinear models using φ-divergence test statistics under product-multinomial sampling

作　　者：金应华[1] 吴耀华[1] 

机构地区：[1]中国科学技术大学统计与金融系,安徽合肥230026

出　　处：《中国科学技术大学学报》2009年第9期897-905,共9页JUSTC

基　　金：Supported by National Natural Science Foundation of China(10871188,10801123);the Knowledge Innovation Programof the Chinese Academy of Sciences(KJCX3-SYW-S02)

摘　　要：考虑了乘积多项抽样下的对数线性模型.在这个模型下,文献[Jin Y H,Wu Y H.Mini mumφ-divergence esti mator and hierarchical testing in log-linear models under product-multinomial sampling.Journal of Statistical Planning and Inference,2009,139:3 488-3 500]用基于-散度和最小-散度估计构造的统计量研究了几类假设检验问题,这其中就有嵌套假设.最小-散度估计是极大似然估计的推广.在上述文献的基础上,给出了其中一类检验的功效函数的渐近逼近公式;另外,还研究了在一列近邻假设下检验统计量的渐近分布.通过模拟研究发现,与Pearson型统计量和对数极大似然比统计量相比,Cressie-Read型检验统计量有差不多的甚至更好的模拟功效和水平.Suppose that discrete data are distributed according to a product-multinomial distribution whose probabilities follow a loglinear model. Under the model above, Ref. [Jin Y H, Wu Y H. Minimum φ-divergence estimator and hierarchical testing in log-linear models under product-multinomial sampling. Journal of Statistical Planning and Inference, 2009, 139：3 488- 3 500] have considered hypothesis test problems including hierarchical tests using φdivergence test statistics that contain the minimum φdivergence estimator （MφE） which is seen as a generalization of the maximum likelihood estimator. Here an approximation to the power function of one of these tests and asymptotic distributions of these test statistics under a contiguous sequence of hypotheses on the basis of the results in Jin et al was gotten. In the last section, a simulation study was conducted to find our member of the power-divergence statistics is the best, the Cressie-Read test statistic is an attractive alternative to the Pearson-based statistic and the likelihood ratio-based test statistic in terms of simulated sizes and powers.

关 键 词：对数线性模型 φ-散度测度 渐近水平 渐近功效 乘积多项抽样 

分 类 号：O212[理学—概率论与数理统计]