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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/69215

    Title: On study of kernel regression function polygons
    Authors: 鄧文舜;Deng, Wen-shuenn;Chu, C.K.
    Contributors: 淡江大學統計學系
    Date: 2000-01-01
    Issue Date: 2011-10-23 16:37:42 (UTC+8)
    Abstract: In the case of the random design nonparametric regression, the regression function estimate is produced practically by joining every two consecutive kernel estimates of regression function values by a straight line segment. Hence, it is of polygon type, and is called the kernel regression function polygon (KRFP) in this paper. The KRFP is analyzed by its asymptotic integrated mean square error (AIMSE). This AIMSE precisely quantifies both effects of the kernel function and of the distance between the points on which kernel estimates of regression function values are calculated on the KRFP. By studying the AIMSE, we have the following findings. First of all, if the distance is of smaller order in magnitude than the bandwidth used by the kernel regression function estimator, then Epanechnikov kernel is still the optimal kernel function for the KRFP. Secondly, if the distance is of the same order in magnitude as the bandwidth, then Epanechnikov kernel is no longer optimal for the KRFP. In this case, using the AIMSE of the KRFP, we obtain the optimal kernel for the KRFP over the class of two-degree polynomials by numerical calculation. As the distance increases, the computation time of the KRFP decreases. However, the resulting performance of the KRFP deteriorates, since the minimum AIMSE of the KRFP over both the bandwidth and the kernel function increases. Finally, if the distance is of larger order in magnitude than the bandwidth, then the uniform kernel is the optimal kernel function for the KRFP.
    Relation: Journal of nonparametric statistics 12(5), pp.597-609
    DOI: 10.1080/10485250008832824
    Appears in Collections:[Graduate Institute & Department of Statistics] Journal Article

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