椭球等高分布族位置参数与刻度参数的点估计与区间估计

POINT AND INTERVAL ESTIMATIONS ON THE LOCATION AND SCALE PARAMETERS OF ELLIPTICALLY CONTURED DISTRIBUTION

一个 p 维随机向量 X=(x_1,…,x_p)′(p≥2),如果服从 p 维椭球等高分布,且具有密度函数,则密度函数一定具有如下形式:f(x)=C_p|∑|^(1/2)g((x-u)′∑^(-1)(x-u)).其中,∑>0,g(·)为某个非负可测函数,且 g(·)

Let X be a p-dimensional random vector with density g(((x-θ1′)A(x-θ1))/σ~2)|A|^(1/2)σ^(-p),where p≥2,x∈R^p,θ∈R^1,σ>0,1=(1,…,1)′_(p×1),A is a known p×ppositive matrix.The shortest interval estimates and equivariant,minimax and admi-ssible point estimates for θ and σ are established.