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Nonparametric estimation of a conditional density

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Abstract

In this paper, we estimate a conditional density. In contrast to standard results in the literature in this context we assume that for each observed value of the covariate we observe a sample of the corresponding conditional distribution of size larger than one. A density estimate is defined taking into account the data from all the samples by computing a weighted average using weights depending on the covariates. The error of the density estimate is measured by the \(L_1\)-error. Results concerning consistency and rate of convergence of the estimate are presented, and the performance of the estimate for finite sample size is illustrated using simulated data. Furthermore, the estimate is applied to a problem in fatigue analysis.

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Acknowledgments

The authors would like to thank the German Research Foundation (DFG) for funding this project within the Collaborative Research Center 666, and two anonymous referees and an associate editor for detailed and very helpful comments improving an early version of the manuscript.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    Ann-Kathrin Bott & Michael Kohler

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  1. Ann-Kathrin Bott
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  2. Michael Kohler
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Correspondence to Ann-Kathrin Bott.

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Bott, AK., Kohler, M. Nonparametric estimation of a conditional density. Ann Inst Stat Math 69, 189–214 (2017). https://doi.org/10.1007/s10463-015-0535-8

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  • DOI: https://doi.org/10.1007/s10463-015-0535-8

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