基于混合样本的污染线性模型的非参数估计

Non-parametric Estimation in Contaminated Linear Model under Mixing Sample

研究污染线性模型 :yi=(1 -ε)xTiβ +zi,1≤i≤n .设误差序列 {zi}是平稳的α 混合序列 ,fε(x)为其公共的未知密度函数 ,在假定Ez2 i<∞的情况下 ,讨论了基于残差的 fε(x)核估计的相合性及其收敛速度 .并构造了污染系数ε及回归参数 β的非参数估计 ,建立了估计量的强相合性及强收敛速度 .

In this paper,we consider the contaminated linear model: y i=(1-ε) x T iβ+z i,1≤i≤n .Let the error sequence ｛ z i ｝ be a stationary α mixing sequence with unknown density f ε(x) .Assuming only the errors have finite moment of order 2,we obtain consistency and convergence rate of the kernel estimation of f ε(x) based on the residuals.Then,we establish non parametric estimation of contaminated coefficient ε and regression parameter β ,and obtain the strong consistency and convergence rate almost surely of the estimators.