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2022 Penalized nonparametric likelihood-based inference for current status data model
Meiling Hao, Yuanyuan Lin, Kin-yat Liu, Xingqiu Zhao
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Electron. J. Statist. 16(1): 3099-3134 (2022). DOI: 10.1214/21-EJS1970

Abstract

Deriving the limiting distribution of a nonparametric estimate is rather challenging but of fundamental importance to statistical inference. For the current status data, we study a penalized nonparametric likelihood-based estimator for an unknown cumulative hazard function, and establish the pointwise asymptotic normality of the resulting nonparametric estimate. We also propose the penalized likelihood ratio tests for local and global hypotheses, derive their limiting distributions, and study the optimality of the global test. Simulation studies show that the proposed method works well compared to the classical likelihood ratio test.

Funding Statement

Meiling Hao’s research is partly supported by the National Natural Science Foundation of China (No. 11901087) and the Program for Young Excellent Talents, UIBE (No. 19YQ15). Yuanyuan Lin’s research is partially supported by the Hong Kong Research Grants Council (Grant No. 14306219 and 14306620) and Direct Grants for Research, The Chinese University of Hong Kong. Xingqiu Zhao’s research is partly supported by the Research Grant Council of Hong Kong (15303319, 15306521) and The Hong Kong Polytechnic University.

Acknowledgments

The authors are grateful to the Editor, the Associate Editor and the anonymous reviewers for their professional review and insightful comments that lead to substantial improvements in the paper.

Citation

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Meiling Hao. Yuanyuan Lin. Kin-yat Liu. Xingqiu Zhao. "Penalized nonparametric likelihood-based inference for current status data model." Electron. J. Statist. 16 (1) 3099 - 3134, 2022. https://doi.org/10.1214/21-EJS1970

Information

Received: 1 August 2020; Published: 2022
First available in Project Euclid: 11 May 2022

Digital Object Identifier: 10.1214/21-EJS1970

Keywords: Current status data , functional Bahadur representation , likelihood ratio test , nonparametric inference , penalized likelihood

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