中国科学技术大学学报
中國科學技術大學學報
중국과학기술대학학보
JOURNAL OF UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA
2009年
9期
897-905
,共9页
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
對數線性模型%φ-散度測度%漸近水平%漸近功效%乘積多項抽樣
대수선성모형%φ-산도측도%점근수평%점근공효%승적다항추양
loglinear model%φ-divergence measure%asymptotic size%asymptotic power%product-multinomial sampling
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.
攷慮瞭乘積多項抽樣下的對數線性模型.在這箇模型下,文獻[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-散度估計構造的統計量研究瞭幾類假設檢驗問題,這其中就有嵌套假設.最小φ-散度估計是極大似然估計的推廣.在上述文獻的基礎上,給齣瞭其中一類檢驗的功效函數的漸近逼近公式;另外,還研究瞭在一列近鄰假設下檢驗統計量的漸近分佈.通過模擬研究髮現,與Pearson型統計量和對數極大似然比統計量相比,Cressie-Read型檢驗統計量有差不多的甚至更好的模擬功效和水平.
고필료승적다항추양하적대수선성모형.재저개모형하,문헌[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]용기우φ-산도화최소φ-산도고계구조적통계량연구료궤류가설검험문제,저기중취유감투가설.최소φ-산도고계시겁대사연고계적추엄.재상술문헌적기출상,급출료기중일류검험적공효함수적점근핍근공식;령외,환연구료재일렬근린가설하검험통계량적점근분포.통과모의연구발현,여Pearson형통계량화대수겁대사연비통계량상비,Cressie-Read형검험통계량유차불다적심지경호적모의공효화수평.
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.
