线性模型中误差分布的相合核估计

ON THE CONGRUENT KERNEL ESTIMATE OF ERROR DISTRIBUTION IN LINEAR MODEL

线性模型y_i=x′_iθ+e_i,i=1…n,的误差序列{e_i}_i^n=1有未知密度f(x),本文在一定条件下证明了f(x)的核估计的弱相合性,逐点强相合性,一致强相合性,其中(?)为L.S估计的残差.

For a Linear Model y1 = xi + ei, i=1-n, the error sequence {ei}ni-1 has an unknow density f(x). The present article proves the weak convergence and the strong local convergence?and the strong uniform convergence of f(x)'s kernel estimate fn(x)= under some condition, of which eni is the residuals of L.S estimate.