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Strong convergence in nonparametric regression with truncated dependent data
Authors:Han-Ying Liang  Deli Li
Institution:a Department of Mathematics, Tongji University, Shanghai 200092, PR China
b Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, Canada P7B 5E1
c Department of Mathematics and Statistics, University of Minnesota-Duluth, 1117 University Drive, Duluth, MN 55812, USA
Abstract:In this paper we derive rates of uniform strong convergence for the kernel estimator of the regression function in a left-truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. The estimation of the covariate’s density is considered as well. Under the assumption that the lifetime observations are bounded, we show that, by an appropriate choice of the bandwidth, both estimators of the covariate’s density and regression function attain the optimal strong convergence rate known from independent complete samples.
Keywords:primary  62G07  secondary  62G20
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