Abstract
Doubly truncated data are commonly encountered in areas like medicine, astronomy, economics, among others. A semiparametric estimator of a doubly truncated random variable may be computed based on a parametric specification of the distribution function of the truncation times. This semiparametric estimator outperforms the nonparametric maximum likelihood estimator when the parametric information is correct, but might behave badly when the assumed parametric model is far off. In this paper we introduce several goodness-of-fit tests for the parametric model. The proposed tests are investigated through simulations. For illustration purposes, the tests are also applied to data on the induction time to acquired immune deficiency syndrome for blood transfusion patients.
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Acknowledgments
Research supported by research Grant MTM2011-23204 (FEDER support included) of the Spanish Ministerio de Ciencia e Innovación, and by SFRH/BPD/68328/2010 Grant of Portuguese Fundação Ciência e Tecnologia. Third author is supported by IAP research network Grant No. P7/06 of the Belgian government (Belgian Science Policy), by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement No. 203650, and by the contract “Projet d’Actions de Recherche Concertées” (ARC) 11/16-039 of the “Communauté française de Belgique” (Granted by the “Académie universitaire Louvain”).
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Moreira, C., de Uña-Álvarez, J. & Van Keilegom, I. Goodness-of-fit tests for a semiparametric model under random double truncation. Comput Stat 29, 1365–1379 (2014). https://doi.org/10.1007/s00180-014-0496-z
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DOI: https://doi.org/10.1007/s00180-014-0496-z