Abstract
It is known that consistent nonparametric regression for a current status censored (CSC) response and a univariate predictor is possible. The paper, for the first time in the literature, presents sharp minimax theory of mean integrated squared error (MISE) convergence and methodology of adaptive estimation. Rate of the MISE convergence is classical, the sharp constant quantifies the effect of CSC, and the results hold under a mild assumption on smoothness of nuisance functions not tied to smoothness of the regression. Then the setting is extended to a multivariate predictor. Real and simulated examples are presented, as well as an illuminating comparison of theoretical results known for CSC and directly observed data.
Funding Statement
The research is supported in part by NSF Grant DMS-1915845 and Grants from CAS and BIFAR.
Acknowledgments
The author would like to thank the editor, Prof. Gang Li, an Associate Editor and the reviewers for valuable comments and suggestions that broaden the scope and improved the quality of this paper.
Citation
Sam Efromovich. "Nonparametric regression for current status censored response." Electron. J. Statist. 18 (2) 4916 - 4991, 2024. https://doi.org/10.1214/24-EJS2321
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