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Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths

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  • Santanu Dutta
  • Koushik Saha

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.

Suggested Citation

  • Santanu Dutta & Koushik Saha, 2017. "Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(6), pages 2708-2723, March.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:6:p:2708-2723
    DOI: 10.1080/03610926.2015.1048886
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