ADMISSIBILITY OF SIMULTANEOUS ESTIMATORS FOR FIRST MOMENT, SECOND MOMENT AND SECOND CENTRAL MOMENT

Consider the model Y=（Y₁, …, Y_n）’=1.β+ε=（β,…,β）’+ （ε₁,…,ε_n）’, where 1=（1, …, 1’）, ε₁,…., ε_n are independent, E（ε_i）=0, E（ε_i²）=σ², E（ε_i³）=0, E（ε_i⁴）=3⁴, i=1, …, n, -∞＜β＜∞, 0＜σ²＜∞. The necessary and sufficient conditions that （Y’A₁Y, Y’A₂Y） and （I’Y, Y’A₁Y, Y’A₂Y） are admissible for （σ²,σ²+β²） and （βσ², σ²+β²） within the olass Y’A₁Y, Y’A₂Y: A₁, A₂≥0 and I’Y, Y’A₁Y, Y’A₂Y:I∈ Rⁿ, A₁, A₂≥0 axe given respeetively. In comparision with the meshed used in other papers, our method is a bit simpler to comfirm or diseonfirm the admissibility of a linear estimator among linear estimators or a quadratio estimator among quadratio estimators.