Consistent Estimation of Residual Density Function in Nonparametric Regression Model Under Dependent Samples
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Graphical Abstract
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Abstract
We consider the nonparametric regression model =g(Xi)+εi, where the residual εi is a stationary φ-mixed process with unknown common density function f(x), g(x) = 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) forg(x), then we construct the estimate \widehatf_n(x) for f(x)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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