Fan, Jianqing; Gijbels, Irène Variable bandwidth and local linear regression smoothers. (English) Zbl 0765.62040 Ann. Stat. 20, No. 4, 2008-2036 (1992). Summary: We introduce an appealing nonparametric method for estimating the mean regression function. The proposed method combines the ideas of local linear smoothers and variable bandwidth. Hence, it also inherits the advantages of both approaches. We give expressions for the conditional MSE and MISE of the estimator. Minimization of the MISE leads to an explicit formula for an optimal choice of the variable bandwidth.Moreover, the merits of considering a variable bandwidth are discussed. In addition, we show that the estimator does not have boundary effects, and hence does not require modifications at the boundary. The performance of a corresponding plug-in estimator is investigated. Simulations illustrate the proposed estimation method. Cited in 5 ReviewsCited in 166 Documents MSC: 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 62J99 Linear inference, regression Keywords:mean squared error; nonparametric regression; optimalities; mean integrated squared error; simulations; mean regression function; local linear smoothers; variable bandwidth; conditional MSE; MISE; boundary effects; plug-in estimator × Cite Format Result Cite Review PDF Full Text: DOI