对数线性模型下基于Φ-散度测度的均值滑动检验
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摘要
研究了对数线性模型的均值滑动检验.基于Φ-散度和最小Φ-散度估计提出了3类检验统计量,它们是似然比检验统计量和Pearson检验统计量的推广.研究了这3类统计量的渐近分布,并用此理论结果分析了一组实际数据.最后通过模拟研究表明,在小样本量下,这3类统计量中有比似然比检验统计量和Pearson检验统计量表现更好的统计量.
The mean-shift test under the log-linear mode is studied. Based on Φ-divergence and the minimum Φ-divergence estimator, three families of test statistic, which are a generalization of log-likelihood ratio statistic and the Pearson statistic, are proposed. Their asymptotic distribution is presented while they are used to analyze some empirical data. A simulation study is also conducted. And the outcome shows that there are alternatives among these three families of test statistic as good as(or even better than) the log-likelihood ratio statistic and the Pearson statistic under finite sample size.
The mean-shift test under the log-linear mode is studied. Based on Φ-divergence and the minimum Φ-divergence estimator, three families of test statistic, which are a generalization of log-likelihood ratio statistic and the Pearson statistic, are proposed. Their asymptotic distribution is presented while they are used to analyze some empirical data. A simulation study is also conducted. And the outcome shows that there are alternatives among these three families of test statistic as good as(or even better than) the log-likelihood ratio statistic and the Pearson statistic under finite sample size.
引文
[1]PARDO L,PARDO M C.Nonadditivity in log-linear models usingΦ-divergence and MLEs[J].Journal of Statistical Planning and Inference,2005,127(1-2):237-252.
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[8]陈静,刘洋.基于最小熵的流形学习排列方法[J].广东工业大学学报,2015,32(3):39-45.CHEN J,LIU Y.The minimum entropy alignment in manifold learning[J].Journal of Guangdong University of Technology,2015,32(3):39-45.
[9]陈璟华,邱明晋,郭经韬,等.模糊熵权法和CCPSO算法的含风电场电力系统多目标无功优化[J].广东工业大学学报,2018,35(1):35-40.CHEN J H,QIU M J,GUO J T,et al.Multi-objective Reactive power optimization in electric power system with wind farm based on fuzzy entropy weight method and CCPSO algorithm[J].Journal of Guangdong University of Technology,2018,35(1):35-40.
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[11]MORALES D,PARDO L,VAJDA I.Asymptotic divergence of estimates of discrete distribution[J].Journal of Statistical Planning and Inference,1995,48(3):347-369.
[12]CRESSIE N,PARDO L.Model checking in log-linear models usingΦ-divergence and mles[J].Journal of Statistical planning and inference,2002,103(1-2):437-453.
[13]CRESSIE N,PARDO L,PARDO M.Size and power consideration for testing log-linear models usingΦ-divergence test statistics[J].Statistics Sinica,2003,13(2):555-570.
[14]AGRESTI A.Categorical data analysis[M].New York:John Wiley,1996.
[15]DALE J R.Asymptotic normality of goodness-of-fit statistics for sparse product multinomials[J].Journal of the Royal Statistical Society Series.B,1986,48(1):48-59.
[16]MARTIN N,PARDO L.New families of estimators and test statistics in log-linear models[J].Journal of Multivariate Analysis,2008,99(8):1590-1609.
[17]MARTIN N,MATA R,PARDO L.Phi-divergence statistics for the likelihood ratio order:An approach based on the log-linear models[J].Journal of Multivariate Analysis,2014,130:387-408.
[18]王松桂,史建红,尹素菊,吴密霞.线性模型引论[M].北京:科学出版社,2004.
[2]JIN Y H,MING R X,WU Y H.Nonadditivity in log-linear model usingΦ-divergence and MΦEs under product-multinomial sampling[J].Journal of Statistical Planning and Inference,2013,143(2):356-367.
[3]CHRISTENSEN R.Loglinear model and logistic regression[M].second ed.New York:Springer-Verlag,1997.
[4]JIN Y H,WU Y H.MinimumΦ-divergence estimator and hierarchical testing in loglinear models under product-multinomial sampling[J].Journal of Statistical Planning and Inference,2009,139(10):3488-3500.
[5]ALI S M,SILVEY S D.A general class of coefficient of divergence of one distribution from another[J].Journal of Royal Statistical Society,Series B,1966,28(1):131-142.
[6]CSISZAR I.Information type measures of dif-ference of probability distributions and indirect observations[J].Studia Scientiarum Mathematicarum Hungarica,1967,2(2):299-318.
[7]CRESSIE N,READ T.Multinomial goodness-of-fit tests[J].Journal of the Royal Statistical Society,1984,46(3):440-464.
[8]陈静,刘洋.基于最小熵的流形学习排列方法[J].广东工业大学学报,2015,32(3):39-45.CHEN J,LIU Y.The minimum entropy alignment in manifold learning[J].Journal of Guangdong University of Technology,2015,32(3):39-45.
[9]陈璟华,邱明晋,郭经韬,等.模糊熵权法和CCPSO算法的含风电场电力系统多目标无功优化[J].广东工业大学学报,2018,35(1):35-40.CHEN J H,QIU M J,GUO J T,et al.Multi-objective Reactive power optimization in electric power system with wind farm based on fuzzy entropy weight method and CCPSO algorithm[J].Journal of Guangdong University of Technology,2018,35(1):35-40.
[10]PARDO L,PARDO M C.Minimum power-divergence estimator in threeway contingency tables[J].Journal of Statistical Computation and Simulation,2003,73(11):819-831.
[11]MORALES D,PARDO L,VAJDA I.Asymptotic divergence of estimates of discrete distribution[J].Journal of Statistical Planning and Inference,1995,48(3):347-369.
[12]CRESSIE N,PARDO L.Model checking in log-linear models usingΦ-divergence and mles[J].Journal of Statistical planning and inference,2002,103(1-2):437-453.
[13]CRESSIE N,PARDO L,PARDO M.Size and power consideration for testing log-linear models usingΦ-divergence test statistics[J].Statistics Sinica,2003,13(2):555-570.
[14]AGRESTI A.Categorical data analysis[M].New York:John Wiley,1996.
[15]DALE J R.Asymptotic normality of goodness-of-fit statistics for sparse product multinomials[J].Journal of the Royal Statistical Society Series.B,1986,48(1):48-59.
[16]MARTIN N,PARDO L.New families of estimators and test statistics in log-linear models[J].Journal of Multivariate Analysis,2008,99(8):1590-1609.
[17]MARTIN N,MATA R,PARDO L.Phi-divergence statistics for the likelihood ratio order:An approach based on the log-linear models[J].Journal of Multivariate Analysis,2014,130:387-408.
[18]王松桂,史建红,尹素菊,吴密霞.线性模型引论[M].北京:科学出版社,2004.