Abstract
Nonparametric maximum likelihood estimators (MLEs) in inverse problems often have non-normal limit distributions, like Chernoff’s distribution. However, if one considers smooth functionals of the model, with corresponding functionals of the MLE, one gets normal limit distributions and faster rates of convergence. We demonstrate this for a model for the incubation time of a disease. The usual approach in the latter models is to use parametric distributions, like Weibull and gamma distributions, which leads to inconsistent estimators. Smoothed bootstrap methods are discussed for constructing confidence intervals.
Acknowledgements
I want to thank the referees for their constructive remarks. I also want to thank Geurt Jongbloed for useful discussions.
Citation
Piet Groeneboom. "Nonparametric estimation of the incubation time distribution." Electron. J. Statist. 18 (1) 1917 - 1969, 2024. https://doi.org/10.1214/24-EJS2243
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