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Multivariate density estimation using dimension reducing information and tail flattening transformations for truncated or censored data

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Abstract

This paper introduces a multivariate density estimator for truncated and censored data with special emphasis on extreme values based on survival analysis. A local constant density estimator is considered. We extend this estimator by means of tail flattening transformation, dimension reducing prior knowledge and a combination of both. The asymptotic theory is derived for the proposed estimators. It shows that the extensions might improve the performance of the density estimator when the transformation and the prior knowledge is not too far away from the true distribution. A simulation study shows that the density estimator based on tail flattening transformation and prior knowledge substantially outperforms the one without prior knowledge, and therefore confirms the asymptotic results. The proposed estimators are illustrated and compared in a data study of fire insurance claims.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen Ø, Denmark

    Tine Buch-Kromann

  2. Cass Business School, City University London, 106 Bunhill Row, London, EC1Y 8TZ, UK

    Jens Perch Nielsen

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  1. Tine Buch-Kromann
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  2. Jens Perch Nielsen
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Correspondence to Tine Buch-Kromann.

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Buch-Kromann, T., Nielsen, J.P. Multivariate density estimation using dimension reducing information and tail flattening transformations for truncated or censored data. Ann Inst Stat Math 64, 167–192 (2012). https://doi.org/10.1007/s10463-010-0313-6

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  • DOI: https://doi.org/10.1007/s10463-010-0313-6

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