随机删失数据下极大似然估计量的性质
|
摘要
研究了观察数据被随机删失时,极大似然估计的局部渐近正态性与渐近极小极大有效性,建立了局部渐近正态成立的充分条件,并给出渐近极小极大风险的下界以及达到该下界的充分必要条件,证明了随机删失下参数极大似然估计的渐近极小极大有效性.
In this paper, we study the local asymptotic normality and asymptotic minimax validity of maximum likelihood estimators when observational data are randomly censored. Sufficient conditions for the existence of local asymptotic normality are established. The lower bound of asymptotic minimax risk and sufficient and necessary conditions for reaching the lower bound are given. The asymptotic minimax validity of parametric maximum likelihood estimators under random censorship is proved.
In this paper, we study the local asymptotic normality and asymptotic minimax validity of maximum likelihood estimators when observational data are randomly censored. Sufficient conditions for the existence of local asymptotic normality are established. The lower bound of asymptotic minimax risk and sufficient and necessary conditions for reaching the lower bound are given. The asymptotic minimax validity of parametric maximum likelihood estimators under random censorship is proved.
引文
[1] LECAM L. On the assumptions used to prove asymptotic normality of maximum likelihood estimators[J]. Annals of Mathematical Statistics,1970,41(3):802-828.
[2] KUTOYANTS Y A, MOURID T, BOSQ D. Local asymptotic minimax and admissibility in estimation[J].Análisis Financiero,1992, 28 (1) :18-30
[3] IBRAGIMOV I A, HAS’MINSKII R Z. Statistical Estimation[M].New York: Springer Verlag,1981:410-421.
[4] WALD A. Note on the consistency of the maximum likelihood estimate[J]. Ann Math Statist, 1949,20 (2):595-601.
[5] SHORACK G R, WELLNER J A. Empir ical processes with applications to statistics[M]. New York: John Wiley & Sons,1987.
[6] SAUNDERS S C, MYHRE J M. On the behavior of certain maximum like- lihood estimators from large, randomly censored samples[J]. J Amer Statist Assoc,1984,79(836):294-301.
[7] POLSHKOV, YULIAN N. Quasi- maximal likelihood estimator of the unknown parameter in systems with “physical” white noise[J]. Random Oper Stochastic Equations,2001(9):263-274.
[8] 张成毅,罗双华.缺失数据下局部估计的弱相合性和渐近正态性[J].纺织高校基础科学学报,2012,25(1):9-12.
[9] 涂冬生.混合截尾似然比的局部渐近正态性及应用[J].应用概率统计,1988,4(2):113-119.
[10] 罗双华,庞淑侠.缺失数据下局部M-估计的相合性和渐近正态性[J].兰州理工大学学报,2006,32(5):145-148.
[2] KUTOYANTS Y A, MOURID T, BOSQ D. Local asymptotic minimax and admissibility in estimation[J].Análisis Financiero,1992, 28 (1) :18-30
[3] IBRAGIMOV I A, HAS’MINSKII R Z. Statistical Estimation[M].New York: Springer Verlag,1981:410-421.
[4] WALD A. Note on the consistency of the maximum likelihood estimate[J]. Ann Math Statist, 1949,20 (2):595-601.
[5] SHORACK G R, WELLNER J A. Empir ical processes with applications to statistics[M]. New York: John Wiley & Sons,1987.
[6] SAUNDERS S C, MYHRE J M. On the behavior of certain maximum like- lihood estimators from large, randomly censored samples[J]. J Amer Statist Assoc,1984,79(836):294-301.
[7] POLSHKOV, YULIAN N. Quasi- maximal likelihood estimator of the unknown parameter in systems with “physical” white noise[J]. Random Oper Stochastic Equations,2001(9):263-274.
[8] 张成毅,罗双华.缺失数据下局部估计的弱相合性和渐近正态性[J].纺织高校基础科学学报,2012,25(1):9-12.
[9] 涂冬生.混合截尾似然比的局部渐近正态性及应用[J].应用概率统计,1988,4(2):113-119.
[10] 罗双华,庞淑侠.缺失数据下局部M-估计的相合性和渐近正态性[J].兰州理工大学学报,2006,32(5):145-148.