Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths |
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Authors: | Santanu Dutta Koushik Saha |
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Affiliation: | 1. Mathematical Science Department, Tezpur University, Napaam, Tezpur, Assam, India;2. Department of Mathematics, IIT Bombay, Mumbai, India |
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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. |
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Keywords: | Multivariate kernel density estimator random bandwidth |
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