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B0279
Title: Uniform in bandwidth convergence rate of the kernel regression estimator adaptive to intrinsic dimension Authors:  Thouria El Hadjali - Universite de Technologie de Compiegne (France) [presenting]
Salim Bouzebda - Universite de Technologie de Compiegne (France)
Boutheina Nemouchi - Universite de Technologie de Compiegne (France)
Abstract: The focus is on the uniform in bandwidth consistency of kernel-type regression estimators of the regression function $\mathbb{E}(\Psi(\mathbf{Y})\mid \mathbf{\mathbf{ X}}=\mathbf{ x})$ derived by modern empirical process theory, under weaker conditions on the kernel than previously used in the literature. Our theorems allow data-driven local bandwidths for these statistics. We extend existing uniform bounds on kernel regression estimator and making it adaptive to the intrinsic dimension of the underlying distribution of $\mathbf{X}$ which will be characterizing by the so-called intrinsic dimension. Moreover, we show, in the same context, the uniform in bandwidth consistency for nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship.