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Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths
Authors:Santanu Dutta  Koushik Saha
Affiliation:1. Mathematical Science Department, Tezpur University, Napaam, Tezpur, Assam, India;2. Department of Mathematics, IIT Bombay, Mumbai, India
Abstract:
We obtain the rates of pointwise and uniform convergence of multivariate kernel density estimators using a random bandwidth vector obtained by some data-based algorithm. We are able to obtain faster rate for pointwise convergence. The uniform convergence rate is obtained under some moment condition on the marginal distribution. The rates are obtained under i.i.d. and strongly mixing type dependence assumptions.
Keywords:Multivariate kernel density estimator  random bandwidth
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