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

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. 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]用基于φ-散度和最小φ-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φ-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 φ-divergence test statistics that contain the minimum φ-divergence 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.