Consistency of multivariate density estimators using random bandwidths

Santanu Dutta and Koushik Saha

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 2, 252-266

Abstract: Asymptotic properties of a kernel density estimator using a random bandwidth are difficult to establish. Under some assumptions we prove the L1 consistency of a class of multivariate kernel density estimators using different bandwidth vector selectors. The expected L1 distance between such an estimator and the density is also shown to converge to zero. Our results hold even when the marginal densities are heavy-tailed. As a special case, we propose a simple estimator that depends on only one parameter, irrespective of the dimension. Its L1 distance from the density goes to zero, exponentially. Simulations suggest that this estimator performs well in terms of the integrated squared error as well.

Date: 2016
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DOI: 10.1080/03610926.2013.830747

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