DATA-DRIVEN BANDWIDTH SELECTION IN LOCAL POLYNOMIAL FITTING - VARIABLE BANDWIDTH AND SPATIAL ADAPTATION

• 成果类型: Article
• 署名作者: FAN, JQ; GIJBELS, I
• 署名单位: Universite Catholique Louvain; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• 发表日期: 1995
• 页码: 371-394
• 关键词: linear-regression smoothers; kernel density-estimation; Nonparametric Regression; noisy data; CHOICE

摘要

When estimating a mean regression function and its derivatives, locally weighted least squares regression has proven to be a very attractive technique. The present paper focuses on the important issue of how to select the smoothing parameter or bandwidth. In the case of estimating curves with a complicated structure, a variable bandwidth is desirable. Furthermore, the bandwidth should be indicated by the data themselves. Recent developments in nonparametric smoothing techniques inspired us to propose such a data-driven bandwidth selection procedure, which can be used to select both constant and variable bandwidths. The idea is based on a residual squares criterion along with a good approximation of the bias and variance of the estimator. The procedure can be applied to select bandwidths not only for estimating the regression curve but also for estimating its derivatives. The resulting estimation procedure has the necessary flexibility for capturing complicated shapes of curves. This is illustrated via a large variety of testing examples, including examples with a large spatial variability. The results are also compared with wavelet thresholding techniques, and it seems that our results are at least comparable, i.e. local polynomial regression using our data-driven variable bandwidth has spatial adaptation properties that are similar to wavelets.