QIN Gengsheng, JIANG Zeyun. Consistent Estimation of Residual Density Function in Nonparametric Regression Model Under Dependent Samples[J]. Chinese Journal of Applied Probability and Statistics, 1995, 11(4): 371-377.
Citation: QIN Gengsheng, JIANG Zeyun. Consistent Estimation of Residual Density Function in Nonparametric Regression Model Under Dependent Samples[J]. Chinese Journal of Applied Probability and Statistics, 1995, 11(4): 371-377.

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

  • 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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