教師資料查詢 | 類別: 期刊論文 | 教師: 鄧文舜 Deng Wen-shuenn (瀏覽個人網頁)

標題:An interpolation method for adapting to sparse design in multivariate nonparametric regression
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出版(發表)日期2003/09/01
作品名稱An interpolation method for adapting to sparse design in multivariate nonparametric regression
作品名稱(其他語言)
著者Chu, C. K.; 鄧文舜; Deng, Wen-shuenn
單位淡江大學統計學系
出版者Elsevier
著錄名稱、卷期、頁數Journal of Statistical Planning and Inference 116(1), pp.91-111
摘要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.
關鍵字Interpolation method; Local linear estimator; Nadaraya–Watson estimator; Nonparametric regression; Pseudodata; Sparse design
語言英文
ISSN0378-3758
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國別中華民國
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