Adaptive density estimation based on real and artificial data

Tina Felber, Michael Kohler and Adam Krzyżak

Journal of Nonparametric Statistics, 2015, vol. 27, issue 1, 1-18

Abstract: Let X, X 1 , X 2 , ... be independent and identically distributed ℝ-super- d -valued random variables and let m :ℝ-super- d →ℝ be a measurable function such that a density f of Y = m ( X ) exists. The problem of estimating f based on a sample of the distribution of ( X,Y ) and on additional independent observations of X is considered. Two kernel density estimates are compared: the standard kernel density estimate based on the y -values of the sample of ( X,Y ), and a kernel density estimate based on artificially generated y -values corresponding to the additional observations of X . It is shown that under suitable smoothness assumptions on f and m the rate of convergence of the L 1 error of the latter estimate is better than that of the standard kernel density estimate. Furthermore, a density estimate defined as convex combination of these two estimates is considered and a data-driven choice of its parameters (bandwidths and weight of the convex combination) is proposed and analysed.

Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1080/10485252.2014.969729

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