比例平均剩余寿命模型若干问题的研究
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摘要
本文分别研究了动态比例平均剩余寿命和不完全信息比例平均剩余寿命这两类模型的年龄性质、随机序以及未知参数的极大似然估计的大样本性质.
首先,我们研究了满足动态比例平均剩余寿命模型的两个非负随机变量的年龄性质的若干封闭性及其随机比较.与其它基于生存函数和危险率函数的文献不同,我们的研究主要是基于平均剩余寿命函数.在文中,我们给出了满足动态比例平均剩余寿命模型的两个非负随机变量具有各种相同年龄性质和随机序的若干充分条件,并通过反例说明这些条件一般也是必要的.
其次,我们对不完全信息随机右删失数据下的比例平均剩余寿命模型未知参数的极大似然估计进行了研究.比例平均剩余寿命模型是生存分析里重要的回归模型之一,不完全信息随机右删失数据是生存分析里常见的数据类型,因此研究不完全信息随机右删失的比例平均剩余寿命模型十分有意义.目前尚未见到有文献涉及不完全信息随机右删失数据下比例平均剩余寿命模型的研究,该模型的极大似然估计的极限性质尚属未知.本文在一定的假设下,得到了不完全信息随机右删失的比例平均剩余寿命模型的未知参数极大似然估计的存在性,相合性和渐近正态性.
最后,我们研究了不完全信息随机右删失数据下比例平均剩余寿命模型未知参数的极大似然估计的精细极限行为,证明了此模型下多维未知参数极大似然估计满足重对数律,Chung重对数律及中偏差.
In this paper,the aging properties and stochastic orders for dynamic proportional mean residual life model are investigated,and the large-sample theory of MLE of parameter for proportional mean residual life model with incomplete information is discussed.
First,we study some closure properties of aging properties and stochastic comparisons for two random variables satisfied dynamic proportional mean residual life model.Distinguished from literatures based on survival function or hazard rate function,Our research is based on the mean residual life function.In this paper,we present the sufficient conditions which certify the same aging properties and Stochastic orders of two random variables satis-fied dynamic proportional mean residual life model,and we provide the illustrations which prove that conditions are necessary.
Second,we discuss the MLE of parameter based on the data with random censorship and incomplete information. In survival analysis the proportional mean residual life model is a significant regression model and the right censoring data with incomplete information is a common data type. The research on proportional mean residual life model randomly censored with incomplete information is very meaningful.The proportional mean residual life model based on the data with random right censorship and incomplete information isn't discussed in the existent literatures. Under suitable assumptions, we obtain the existence,consistency, asymptotic normality.
Finally,the law of iterated logarithm,the Chung type law of iterated logarithm and the moderate deviation of MLE of unknown parameters under the model are obtained.
首先,我们研究了满足动态比例平均剩余寿命模型的两个非负随机变量的年龄性质的若干封闭性及其随机比较.与其它基于生存函数和危险率函数的文献不同,我们的研究主要是基于平均剩余寿命函数.在文中,我们给出了满足动态比例平均剩余寿命模型的两个非负随机变量具有各种相同年龄性质和随机序的若干充分条件,并通过反例说明这些条件一般也是必要的.
其次,我们对不完全信息随机右删失数据下的比例平均剩余寿命模型未知参数的极大似然估计进行了研究.比例平均剩余寿命模型是生存分析里重要的回归模型之一,不完全信息随机右删失数据是生存分析里常见的数据类型,因此研究不完全信息随机右删失的比例平均剩余寿命模型十分有意义.目前尚未见到有文献涉及不完全信息随机右删失数据下比例平均剩余寿命模型的研究,该模型的极大似然估计的极限性质尚属未知.本文在一定的假设下,得到了不完全信息随机右删失的比例平均剩余寿命模型的未知参数极大似然估计的存在性,相合性和渐近正态性.
最后,我们研究了不完全信息随机右删失数据下比例平均剩余寿命模型未知参数的极大似然估计的精细极限行为,证明了此模型下多维未知参数极大似然估计满足重对数律,Chung重对数律及中偏差.
In this paper,the aging properties and stochastic orders for dynamic proportional mean residual life model are investigated,and the large-sample theory of MLE of parameter for proportional mean residual life model with incomplete information is discussed.
First,we study some closure properties of aging properties and stochastic comparisons for two random variables satisfied dynamic proportional mean residual life model.Distinguished from literatures based on survival function or hazard rate function,Our research is based on the mean residual life function.In this paper,we present the sufficient conditions which certify the same aging properties and Stochastic orders of two random variables satis-fied dynamic proportional mean residual life model,and we provide the illustrations which prove that conditions are necessary.
Second,we discuss the MLE of parameter based on the data with random censorship and incomplete information. In survival analysis the proportional mean residual life model is a significant regression model and the right censoring data with incomplete information is a common data type. The research on proportional mean residual life model randomly censored with incomplete information is very meaningful.The proportional mean residual life model based on the data with random right censorship and incomplete information isn't discussed in the existent literatures. Under suitable assumptions, we obtain the existence,consistency, asymptotic normality.
Finally,the law of iterated logarithm,the Chung type law of iterated logarithm and the moderate deviation of MLE of unknown parameters under the model are obtained.
引文
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[7]Zahedi,H., Proportional mean residual life model. Journal of Statistical Planning and Inference, 29(1991),221-228.
[8]Gangaji Maguluri and Cun-Hui Zhang,Estimation in the mean residual life regression model, Journal of the Royal Statistical Society(Series B),1994,56(3),477-489.
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[10]Inglot,T.and Kallenberg,W.C.M.,Moderate daviation of minimum contrast estimators under contamination. Ann. Statist.,31(2003),852-879.
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[19]Nanda,A.K.,Bhattacharjee,S.,Alam,s.s.,Properties of proportional mean residual life model. Statistics and Probability Letters,76(2006),880-890.
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[22]Gupta,R.C.,Kirmani,S.,Stochastic comparisons in frailty models. Journal of Statistical Plan-ning and Inference,136(2006),3647-3658.
[23]Chen,Y.Q.,Cheng,S.,Semiparametric regression analysis of mean residual life with censored survival data. Biometrike,92(2005),19-29.
[24]Y.Q.Chen,N.P.Jewell,X.Lei,S.C.Cheng,Semiparametric estimation of proportional mean resid-ual life model in presence of censoring. Biometrike,61(2005),170-178.
[25]Shaked, Shanthikumar,Stochastic Order[M]. Berlin:Springer,2007.
[26]Wang Zhonghai,Chen Yurong,Liu Luqin,Moderate deviations for the maximum likelihood estimator of proportional hazards model with incomplete information,Data Processing and Quantitative Economy Modeling. AUSSINO ACADEMIC PUBLISHING HOUSE,Sydney Australia,2010,606-617.
[27]Liuquan Sun,Zhigang Zhang,A Class of Transformed Mean Residual Life Models With Cen-sored Survival Data,J Am Stat Assoc,104(486)2009,803-815.
[28]Blum,J.R.,Susarla,V.,Maximal Deviation Theory of Density and Failure Rate Function Esti-mates Based on Censored Data, Multivariate Analysis,1980,V,213-222, North-holland Ams-terdam. (P.R.Krishnaiah, Ed.)
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[33]Xiaohu Li,Ming J. Zuo, On the Behaviour of Some New Ageing Properties Based upon the Residual Life of k-out-of-n Systems.Journal of Applied Probability,2(39)2002,426-433.
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[35]Asadi,M., Bairamov,B.,A Note on the Mean Residual Life Function of a Parallel System .Communications in Statistics:Theory and Methods,2(34)2005,475-484.
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