Statistica Sinica

Song Xi Chen

Abstract:This paper proposes beta kernel smoothers for estimating curves with compact support by employing a beta family of densities as kernels. These beta kernel smoothers are free of boundary bias, achieve the optimal convergence rate of for and always allocate non-negative weights. In the context of regression, a comparison is made between one of the beta smoothers and the local linear smoother. Its is comparable with that of the . Situations where the beta kernel smoother has a smaller are given. Extensions to probability density estimation are discussed.

Key words and phrases:Beta kernels, boundary bias, local linear regression, mean integrated square error, nonparametric regression.