摘要
考虑线性回归模型 Y_■=x_4~′β+e_■ i=1,2,…设误差序列■,i≥1满足条件:e_■ i≥1 i.i.d.,Ee_1=0,Ee_1~2=σ~2>0,∞>Var e_1~2=τ~2>0。记■_n^2=1/(n-r){sum from j=1 to n e■-sum from k=1 to r (sum from j=1 to n a_(akj)■_j)~2} δ(n)=τ^(-2)E(■_1~2-σ~2)~2I_((|■-σ~2|≥■τ)+τ^(-3)n^(1/2)|E(■_1~2-σ~2)~3I_((|■_1~2-σ~2|<(nτ)^(1/2))+τ^(-4)n^(-1)E■_1~2-σ~2)~4I_((|■-σ~2|<n^(1/2)τ)) 其中:sum from j=1 to n a_(nlj)a_(nmj)=δ_(lm) n=1,2,…,δ_(lm)是kronecker符号。本文证明了:存在常数C_1,C>0使得■|P(■_n^2-σ~2)/(Var■_n^2)^(1/2))≤x)-Φ(x)|≤C(δ(n)+n^(-1/2)) ■|P(■_n^2-σ~2)/(Var■_n^2)^(1/2))≤x)-Φ(x)|+n^(-1/2)≥C_1δ(n)。
Considering the linear regression model Y_i=x_i'β+e_i i=1, 2,…. Suppose that e_i i≥1 be i.i.d, random Variables with Ee_1=0, Ee_1~2=σ~2>0, ∞>Var e_1~2=τ~■>0. Let ■_n^2=1/(n-r){sum from j=1 to n e_j^2-sum from k=1 to r(sum from j=1 to n a_(nkj)e_j)~2}, δ(n)=τ^(-2)E(e_1~2-σ~2)~2I_(|e_1~2-σ~2|≥n^(1/2)τ) +τ^(-3)n^(-1/2)|E(e_1~2-σ~2)~3I_(|e_1~2-σ~2|<n^(1/2)τ)+τ^(-4)n^(-1)E(e_1~2-θ~2)~4I_(|e_1~2-σ~2|<n^(1/2)τ) where sum from j=1 to n a_(alj)a_(amj)=δ_(lm) and δ_(lm) is kronecker sign. In this paper, we prove that there exist real numbers ∞>C, C_1>0 suth that
出处
《应用概率统计》
CSCD
北大核心
1992年第4期365-373,共9页
Chinese Journal of Applied Probability and Statistics
基金
国家自然科学基金
