线性结构关系模型参数估计的强收敛速度

The Strong Convergent Rate of the Estimation of Parameters in Linear Structural Relationship Model

该文讨论了线性结构关系模型β′ｘｋ＋α＝０ξｋ＝ｘｋ＋εｋｋ＝１，２，…，ｎ｛εｋ，ｋ＝１，２，…，ｎ｝ｉ．ｉ．ｄ．Ｅ（ε１）＝０ｖａｒ（ε１）＝σ２Ｉｍ式中，｛ｘｋ，ｋ＝１，２，…，ｎ｝为一组ｉ．ｉ．ｄ．的不可观测的ｍ维随机向量，｛ｘｋ，ｋ＝１，２，…，ｎ｝与｛εｋ，ｋ＝１，２，…，ｎ｝相互独立。在一些条件下，用重对数律及对称阵特征扰动理论证明了ＬＳ估计量β，α，σ２的强相合性、唯一性，并且给出估计量的强收敛速度为Ｏ（ｎ－１／２（ｌｎｌｎｎ）１／２）。

In this paper the linear structural relationship model β′x k+α=0 ξ k=x k+ε k k=1,2,…,n {ε k ,k=1,2,…,n} i.i.d . E(ε 1)=0 var (ε 1)=σ 2I m is discussed,where {x k ,k=1,2,…,n} is a set of independent identically distributed and unobservable m dimensional random vectors, {x k ,k=1,2,…,n} and {ε k ,k=1,2,…,n} are mutually statistically independent.Under some conditions,the strong consistency and uniqueness of the LS estimator ,, 2 are proved by using the law of the iterated logarithm and characteristic disturbance theory of symmetric matrix,the strong convergent rate of estimators is given by O(n -1/2 ( lnln n) 1/2 ) .