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 consistency results for the generic kernel (including the kernel density estimator) on Riemannian manifolds with Riemann integrable kernels in order to accomplish these difficult tasks. The kernels of the Vapnik-Chervonenkis class that are commonly utilized in statistical problems are different to the isotropic kernels we address in this paper. Moreover, we show, in the same context, the uniform consistency for nonparametric inverse probability of censoring weighted (IPCW) estimators of the regression function under random censorship. As an application, we present the strong uniform consistency for estimators of the Nadaray-Watson type, which is of independent interest.