Abstract: Consider the linear regression model Y_ni=x_niβ＋c_ni,i=1,…,n, where β is the unknown parameter to be estimated, x_ni's are known constants. Assume that, for each n,｛e_n1,…，e_nn｝have the same joint distribution as｛ξ₁，…，ξ_n｝, where ｛ξ_i,t=…，-1,0,1,…｝is strictly stationary and φ-mixing times series defined on a probability space（Ω， B，P） and taking values on R . This paper investigates the asymptotic properties of a class of minimum distance Cramser-Von Mises type estimators of the slope parameterin a linear regression model. These estimators are defined in terms of minimizing an integral of squared difference between weighted empiricals of the residuals and their expectations with respect to a large class of integrating measures. The estimator β_d of β is shown to be asymptotically normal.

Key words: minimum distance estimation, φ-mixing, asymptotic normality

摘要： 考虑线性回归模型 Y_ni=x_niβ+ e_ni,i=1,…，n，其中β是待估计的未知参数，x_ni是已知的常数。假定对每个 n, e_n1，…，e_nn 与ξ₁,…，ξ_n同分布，其中｛ξ_t, t=…，-1，0，1，…｝是定义于概率空间(Ω,B,P)上取值于R的严平稳φ-混合序列。研究了一类由Cramer-von Mises型距离所定义的参数β的最小距离估计的渐进性质。证明了β的估计β_d是渐进正态的。

关键词: 最小距离估计, φ-混合, 渐近正态性