摘要
Ｘ１，…，Ｘｍ；Ｙ１，…，Ｙｎ为独立随机样本，Ｘ，Ｘ１，…，Ｘｍ同分布，Ｘ－Ｆ，Ｆ（０）＝０，Ｙ，Ｙ１，…，Ｙｎｍ同分布，Ｙ的分布函数为Ｇ（ｙ）＝１／μ∫ｙω（ｔ，β）ｄＦ（ｔ），ｙ≥０，其中，β∈Ｒ，μ＝∫０＾∞ω（ｔ，β）ｄＦ（ｔ），０〈μ，ω（ｔ，β）〈∞，Ｆ，μ和β均未知，ω（ｔ，β）的形式已知，设θ为一待估参数，且存在一已知函数ψ（Ｘ，θ）满足ＥＦψ（Ｘ，θ）＝０。
Let X1,…Xm; Y1，…, Yn be independet and suppose the X1,…，Xm are identically distributed as unknown distribution F with F(0)=0 and the Y1,…，Yn are identically distributed aswhere β∈R,μ=∫ω(t,β) dF(t), 0<μ，ω(t,β)<∞， both μand β are unknown, butω(t, β) is of known form. For a unknown parameter θ， we assume that information about θand F is available in the known form as follows:E_Fψ(X,θ)=0.In this paper, the estimates and their asymptotic properties for θ are obtained by using theempirical likelihood method, which partly solves a open problem in biased models.
出处
《应用数学学报》
CSCD
北大核心
1998年第3期428-436,共9页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金
国家教委博士点基金
关键词
有偏模型
统计泛函
渐近分布
经验似然估计
Biased models, statistical functionals, empirical likelihood,asymptotic distributions
