随机删失下指数分布参数MLE的一些结果(英文)

Some Results on MLE of the Parameter of the Exponential Distribution from Randomly Censored Data

考虑指数总体F(x ,θ) =1-e- xθ, x≥ 0 ,其中θ >0是未知参数。本文证明基于随机删失观察的参数θ的MLEθ^n 是渐近minimax有效的 ,即对某损失函数W (·) ,limδ→ 0 limn→∞ sup｜θ′-θ｜<δE(n)θ′ {w[- 1(n) (θ^n-θ) ]} =Ew(ξ) ,其中 ,L(ξ) =N(0 ,1) ,p(n) =(nI|θ|) - 12 ,I(θ)是删失观察的信息函数。此外 ,还建立了重对数律及θ^n 的r(≥ 2 )阶均方误差不等式。

Consider the exponential population\$\$F(x,θ)=1-e-- -xθ,\ x≥0,\$\$where θ>0 is an unknown parameter.In this paper the MLE of θ,say θ^\-n,from randomly censored data is pr oved to be asymptotic minimax efficiency.That is,for a certain loss function w(·),\$\$ limδ→0 limn→∞ sup|θ′-θ|<δE- (n) θ′{w\[- -1(n)(θ[DD(-1]^\-n-θ′)\]}=Ew(ξ),\$\$where }=Ew(ξ),\$\$where L(ξ)=N(0,1),(n)=(nI(θ))-- -12 and I(θ) is the information function of the censored observations.Furthermor e,the iterative logarithm law and an inequality for the rth(r≥2) mean error of θ^\-n are also established,respectivel y.