含辅助信息的最小非参似然比估计和检验
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摘要
当前,拟合优度检验已经比较完善,但仍存在对总体分布已有信息利用不足或者直接丢掉这部分信息的问题.为了实现对已有信息的充分利用,首先借助经验似然的思想与最小非参似然比统计量的形式,给出含辅助信息的最小非参似然比统计量;然后利用最小非参似然比估计与检验性质的研究方法,得到含辅助信息的最小非参似然比估计量,并考察检验统计量的相合性、稳健性,同时得到其在复合零假设下的极限分布.这些结论在一定程度上可以丰富和完善拟合优度检验与非参数估计的一些理论.
Currently,though the goodness of fit test is already fairly complete,there are still existing some outstanding problems,which will be lack of existing information or losing partly information directly during estimating the distribution. In order to achieve full utilization of existing information,first of all,with the idea of empirical likelihood and the form of minimum non-parametric likelihood ratio statistic,the paper gives the minimum nonparametric likelihood ratio statistic with the presence of auxiliary information. Then,using a minimum non-parametric likelihood ratio estimation and testing methods,the minimum nonparametric likelihood ratio estimator with the presence of auxiliary information is obtained. At last,the feature of consistency and robustness are studied,at the same time,the limit distribution in composite null hypothesis is got. To some extent,these conclusions can enrich and improve the theories of goodness testing and the nonparametric estimation.
Currently,though the goodness of fit test is already fairly complete,there are still existing some outstanding problems,which will be lack of existing information or losing partly information directly during estimating the distribution. In order to achieve full utilization of existing information,first of all,with the idea of empirical likelihood and the form of minimum non-parametric likelihood ratio statistic,the paper gives the minimum nonparametric likelihood ratio statistic with the presence of auxiliary information. Then,using a minimum non-parametric likelihood ratio estimation and testing methods,the minimum nonparametric likelihood ratio estimator with the presence of auxiliary information is obtained. At last,the feature of consistency and robustness are studied,at the same time,the limit distribution in composite null hypothesis is got. To some extent,these conclusions can enrich and improve the theories of goodness testing and the nonparametric estimation.
引文
[1]陈希孺,方兆本,李国英,等.非参数统计[M].合肥:中国科学技术大学出版社,2012.
[2]李裕奇,赵联文,王沁,等.非参数统计方法[M].成都:西南交通大学出版社,2010.
[3]BERK R H,JONES D H.Goodness-of-fit statistics that dominate the Kolmogorov statistics[J].Z Wahrsch-Verw Gebiete,1979,47:47-59.
[4]ZHANG J.Power full goodness-of-fit tests on the likelihood ratio[J].J Royal Statistical Society Soc,2002,B64(2):281-294.
[5]张军舰,杨振海,程维虎.拟合优度检验[M].北京:科学出版社,2010.
[6]张军舰,李国英.上界型拟合优度检验[J].数学物理学报,2010(2):344-357.
[7]JAGER L,WELLNER J A.A New Goodness of Fit Test:the Reversed Berk-Jones Statistic[M].Seattle:University of Washington,2004:1-21.
[8]ZHANG B.M-estimation and quantile estimation in the presence of auxiliary information[J].J Statistical Planning and Inference,1995,44:77-94.
[9]ZHANG B.Confidence intervals for a distribution function in the presence of auxiliary information[J].Comput Statistics Data Analysis,1996,21:327-342.
[10]FENG L X,LI R.Smoothed empirical likelihood confidence intervals for quantile regression parameters with auxiliary information[J].Statistical Methodology,2013,15:46-54.
[11]OWEN A B.Empirical likelihood ratio confidence intervals for a single function[J].Biometrika,1988,75(2):237-249.
[12]OWEN A B.Non parametric Likelihood Confidence Bands for a Distribution Function[J].J Am Statistical Association,1995,90:516-521.
[13]林正炎,陆传荣,苏中根.概率极限理论基础[M].北京:高等教育出版社,1999.
[14]许宝,姜玉秋,藤飞.一种加权对称损失函数下一类指数分布模型参数的估计[J].四川师范大学学报(自然科学版),2011,34(4):484-487.
[15]张军舰.广义非参似然比拟合优度检验[D].北京:中国科学院,2006.
[16]POLLARD D.The minimum distance method of testing[J].Metrikea,1980,27:43-70.
[2]李裕奇,赵联文,王沁,等.非参数统计方法[M].成都:西南交通大学出版社,2010.
[3]BERK R H,JONES D H.Goodness-of-fit statistics that dominate the Kolmogorov statistics[J].Z Wahrsch-Verw Gebiete,1979,47:47-59.
[4]ZHANG J.Power full goodness-of-fit tests on the likelihood ratio[J].J Royal Statistical Society Soc,2002,B64(2):281-294.
[5]张军舰,杨振海,程维虎.拟合优度检验[M].北京:科学出版社,2010.
[6]张军舰,李国英.上界型拟合优度检验[J].数学物理学报,2010(2):344-357.
[7]JAGER L,WELLNER J A.A New Goodness of Fit Test:the Reversed Berk-Jones Statistic[M].Seattle:University of Washington,2004:1-21.
[8]ZHANG B.M-estimation and quantile estimation in the presence of auxiliary information[J].J Statistical Planning and Inference,1995,44:77-94.
[9]ZHANG B.Confidence intervals for a distribution function in the presence of auxiliary information[J].Comput Statistics Data Analysis,1996,21:327-342.
[10]FENG L X,LI R.Smoothed empirical likelihood confidence intervals for quantile regression parameters with auxiliary information[J].Statistical Methodology,2013,15:46-54.
[11]OWEN A B.Empirical likelihood ratio confidence intervals for a single function[J].Biometrika,1988,75(2):237-249.
[12]OWEN A B.Non parametric Likelihood Confidence Bands for a Distribution Function[J].J Am Statistical Association,1995,90:516-521.
[13]林正炎,陆传荣,苏中根.概率极限理论基础[M].北京:高等教育出版社,1999.
[14]许宝,姜玉秋,藤飞.一种加权对称损失函数下一类指数分布模型参数的估计[J].四川师范大学学报(自然科学版),2011,34(4):484-487.
[15]张军舰.广义非参似然比拟合优度检验[D].北京:中国科学院,2006.
[16]POLLARD D.The minimum distance method of testing[J].Metrikea,1980,27:43-70.