Beta kernel smoothers for regression curves

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 n(-4/5) for mean integrated squared error 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 mean integrated squared error is comparable with that of the local linear smoother. Situations where the beta kernel smoother has a smaller mean integrated squared error are given. Extensions to probability density estimation are discussed.