中文摘要：

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] 用基于仁散度和最小妒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．最小妒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．

英文摘要：

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.