Acta Scientiarum Naturalium Universitatis Pekinensis

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Minimum Distance Estimation in aLinear Regression Model:the φ-mixing Case

YANG Ying   

  1. Department of Probability and Statistics, Peking University, Beijing, 100871
  • Received:1994-12-14 Online:1996-09-20 Published:1996-09-20



  1. 北京大学概率统计系,北京,100871

Abstract: Consider the linear regression model Yni=xniβ+cni,i=1,…,n, where β is the unknown parameter to be estimated, xni's are known constants. Assume that, for each n,{en1,…,enn}have the same joint distribution as{ξ1,…,ξn}, where {ξi,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 βd 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 Yni=xniβ+ eni,i=1,…,n,其中β是待估计的未知参数,xni是已知的常数。假定对每个 n, en1,…,enn 与ξ1,…,ξn同分布,其中{ξt, 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βd是渐进正态的。

关键词: 最小距离估计, φ-混合, 渐近正态性

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