The central limit theorem under semiparametric random censorship models |
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| Institution: | 1. Fachhochschule Aachen, Abteilung Jülich, Ginsterweg 1, Julich 52428, Germany;2. University of Wisconsin, Milwaukee, WI, USA;1. Department of Information Engineering, Electronics and Telecommunications (DIET), “Sapienza” University of Rome, Via Eudossiana 18, 00184 Rome, Italy;2. Department of Engineering, University of Perugia, Via G. Duranti 93, 06125, Perugia, Italy;1. Department of Epidemiology and Public Health, University College London, London, United Kingdom;2. Department of Gerontology, Federal University of São Carlos, São Carlos, Brazil;3. Department of Social Medicine, University of São Paulo, Ribeirão Preto, Brazil;4. Department of Medical-Surgical Nursing, University of São Paulo, Sao Paulo, Brazil;1. Key Laboratory of Tree Breeding and Cultivation of the State Forestry Administration, Research Institute of Forestry, Chinese Academy of Forestry, Beijing 100091, PR China;2. Collaborative Innovation Center of Sustainable Forestry in Southern China, Nanjing Forestry University, Nanjing 210037, PR China;3. Division of Forestry and Natural Resources, West Virginia University, 322 Percival Hall, PO Box 6125, Morgantown, WV 26506, USA |
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| Abstract: | We study integrals for arbitrary Borel-measurable functions with respect to a semiparametric estimator of the distribution function in the random censorship model. Based on a representation of these integrals, which is similar to the one given by Stute for Kaplan–Meier integrals, a central limit theorem is established which generalizes a corresponding result of the Cheng and Lin estimator. It is shown that the semiparametric integral estimator is at least as efficient as the corresponding Kaplan–Meier integral estimator in terms of asymptotic variance if the correct semiparametric model is used. Furthermore, a necessary and sufficient condition for a strict gain in efficiency is stated. Finally, this asymptotic result is confirmed in a small simulation study under moderate sample sizes. |
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