Rates of the Strong Uniform Consistency for the Kernel-Type Regression Function Estimators with General Kernels on Manifolds

In the present paper, we develop strong uniform consistencyresults for the generic kernel (including the kernel densityestimator) on Riemannian manifolds with Riemann integrable kernelsin order to accomplish these difficult tasks. The kernels of theVapnik-Chervonenkis class that are commonly utilized instatistical problems are different to the isotropic kernels weaddress in this paper. Moreover, we show, in the same context, theuniform consistency for nonparametric inverse probability ofcensoring weighted (IPCW) estimators of the regression functionunder random censorship. As an application, we present the stronguniform consistency for estimators of the Nadaray-Watson type,which is of independent interest.