ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR PARAMETERS OF TWO-SIDED TRUNCATION DISTRIBUTION FAMILIES
Laisheng Wei · 1989
Consider the two-sided truncation distrbution families written in the form f(x,θ)dx=w(θ_1, θ_2)h(x)I_([θ_1,θ_2])(x)dx, where θ=(θ_1,θ_2). T(x)=(t_1(x), t_2(x))=(min(x_1,…,x_m), max(x_1, …,x_m)) is a sufficient statistic and its marginal density is denoted by f(t)dμ~T. The prior distribution of θ belongs to the family F={G:∫‖θ‖~2dG(θ)∞}. In this paper, the author constructs the empirical Bayes estimator (EBE) of θ, φ_n (t), by using the kernel estimation of f(t). Under a quite general assumption imposed upon f(t) and h(x), it is shown that φ_n(t) is an asymptotically optimal EBE of θ.