半序约束下一类多变量的估计

The Estimations of a Kind of Multivariate under Semi order Restrictions

本文考虑一类多变量在半序约束θｉｊ１≤θｉｊ２≤…≤θｉｊＫｉ＝１，２，…，Ｉ；ｊ＝１，２，…，Ｊθｉ１ｋ≤θｉ２ｋ≤…≤θｉＪｋｉ＝１，２，…，Ｉ；ｋ＝１，２，…，Ｋθ１ｊｋ≤θ２ｊｋ≤…≤θＩｊｋｊ＝１，２，…，Ｊ；ｋ＝１，２，…，Ｋ（１）的条件下的估计问题。给出三元关系下保序回归的充要条件，讨论了多个正态总体及一类特殊指数分布族的参数在约束（１）下的最大似然估计与保序回归的关系。

The estimations of a kind of multivariate under semi order restrictions are considened, for example: θ ij1 ≤θ ij2 ≤…≤θ ijK \ i=1, 2, …, I j=1, 2, …, J θ i1k ≤θ i2k ≤…≤θ iJk \ i=1, 2, …, I k=1, 2, …, K θ 1jk ≤θ 2jk ≤…≤θ Ijk \ j=1, 2, …, J k=1, 2, …, K(1) \ \ The sufficient and necessary conditions of isotonic regnession under ternary relation are approached here. The relationship between the isotonic regression and the maximum likelihood estimation of the parameters of nomal populations and exponential distribution families of a special kind under restrictions (1) are discussed in this paper.