Abstract
Nonparametric estimators are proposed for the logarithm of the intensity function of some univariate counting processes. An Aalen multiplicative intensity model is specified for our counting process and the estimators are derived by a penalized maximum likelihood method similar to the method introduced by Silverman for probability density estimation. Asymptotic properties of the estimators, such as uniform consistency and normality, are investigated and some illustrative examples from survival theory are analyzed.
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This work was conducted while the author was visiting the Department of Mathematics, University of California at Irvine.
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Antoniadis, A. A penalty method for nonparametric estimation of the intensity function of a counting process. Ann Inst Stat Math 41, 781–807 (1989). https://doi.org/10.1007/BF00057741
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DOI: https://doi.org/10.1007/BF00057741