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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/20720

    Title: An interpolation method for adapting to sparse design in multivariate nonparametric regression
    Authors: Chu, C. K.;鄧文舜;Deng, Wen-shuenn
    Contributors: 淡江大學統計學系
    Keywords: Interpolation method;Local linear estimator;Nadaraya–Watson estimator;Nonparametric regression;Pseudodata;Sparse design
    Date: 2003-09-01
    Issue Date: 2009-11-30 12:57:40 (UTC+8)
    Publisher: Elsevier
    Abstract: In the case of the multivariate random design nonparametric regression, an interpolation method is proposed to overcome the problem of unbounded finite sample variance for the local linear estimator (LLE) using a global bandwidth. This interpolation method simply uses the Nadaraya–Watson estimator with the product “Gaussian” kernel to construct pseudodata on equally spaced partition points of the support of the design density. Then the LLE using the “Epanechnikov” kernel is applied to smooth these equally spaced pseudodata. Our proposed estimator for the multivariate regression function has advantages in both the finite sample and the asymptotic cases. In the finite sample case, it always produces “smooth” regression function estimates, adapts “automatically and smoothly” to regions with sparse design, and has bounded conditional (and unconditional) bias and variance. On the other hand, in the asymptotic case, it has the same mean square error as the LLE. Empirical studies demonstrate that our suggested estimator is competitive with alternatives, in the sense of yielding both smaller sample mean integrated square error and smoother estimates.
    Relation: Journal of Statistical Planning and Inference 116(1), pp.91-111
    DOI: 10.1016/S0378-3758(02)00184-2
    Appears in Collections:[Graduate Institute & Department of Statistics] Journal Article

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