相依样本非参数回归模型误差的相合估计

Consistent Estimation of Residual Density Function in Nonparametric Regression Model Under Dependent Samples

  • 摘要: 考虑非参数回归模型Yi=gXi)+εi,i=1,2,…,其中误差εiφ混合随机变量序列且具有公共的未知密度f(·),gx)=E(Y|X=t)为未知回归函数。本文首先基于g(·)的非参数估计\hatg_n(x)定义残差,然后基于残差构造f(·)的估计\widehatf_n(x),最后在适当条件下建立\widehatf_n(x)的逐点相合性及一致强相合性。

     

    Abstract: We consider the nonparametric regression model =gXi)+εi, where the residual εi is a stationary φ-mixed process with unknown common density function fx), gx) = E(Y|X =x) is the unknown regression function. In this paper, first we define the residuals estimates based on the nonparametric estimator \hatg_n(x) forgx), then we construct the estimate \widehatf_n(x) for fx)on the basis of the residuals, the pointwise weak and strong consistency as well as the uniform strong consistency of \widehatf_n(x) are estabilished under some suitable conditions.

     

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