一种非对称损失下分布函数的最优不变估计

Estimation of Distribution Function Under an Unsymmetrical Loss Fuction

关键词:  非对称损失  连续分布函数  不变估计

Key words:  unsymmetrical loss  continuous distribution function  invariant estimator

摘要:

给定来自一未知连续分布函数F的容量为n的子样x₁,x₂,…,x_n,考虑分布函数F的不变估计问题.在非对称损失函数L(F(t),d(t))=b∫(exp{a[d(t)-F(t)]}-a[d(t)-F(t)]-1)dF(t)和单调变换群下得到F的最优不变估计为d(t,X)=∑_i=0ⁿc_iI(x(i)≤ t ≤ x_(i+1)),其中c_i=1/aln(∫₀¹tⁱ(1-t)^n-idt)/(∫₀¹exp{-at}tⁱ(1-t)^n-idt),a≠0,b>0.

Abstract:

Given a random sample of x₁, x₂, …, x_n size n from an unknown continuous distribution function F, this paper considers the problem of invariant estimator of the continuous distribution function F.Under the unsymmetrical loss function L (F (t), d (t))=b∫ (exp{a[d (t)-F (t)]}-a[d (t)-F (t)]-1)dF (t), we get the best invariant estimator of the continuous distribution function F.