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Shape-constrained estimation for current duration data in cross-sectional studies

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  • Chi Wing Chu

    (City University of Hong Kong Kowloon Tong)

  • Hok Kan Ling

    (Queen’s University Kingston)

Abstract

We study shape-constrained nonparametric estimation of the underlying survival function in a cross-sectional study without follow-up. Assuming the rate of initiation event is stationary over time, the observed current duration becomes a length-biased and multiplicatively censored counterpart of the underlying failure time of interest. We focus on two shape constraints for the underlying survival function, namely, log-concavity and convexity. The log-concavity constraint is versatile as it allows for log-concave densities, bi-log-concave distributions, increasing densities, and multi-modal densities. We establish the consistency and pointwise asymptotic distribution of the shape-constrained estimators. Specifically, the proposed estimator under log-concavity is consistent and tuning-parameter-free, thus circumventing the well-known inconsistency issue of the Grenander estimator at 0, where correction methods typically involve tuning parameters.

Suggested Citation

  • Chi Wing Chu & Hok Kan Ling, 2025. "Shape-constrained estimation for current duration data in cross-sectional studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(3), pages 595-630, July.
    • Handle: RePEc:spr:lifeda:v:31:y:2025:i:3:d:10.1007_s10985-025-09658-x
    DOI: 10.1007/s10985-025-09658-x
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    References listed on IDEAS

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    1. Piet Groeneboom & Geurt Jongbloed & Jon A. Wellner, 2008. "The Support Reduction Algorithm for Computing Non‐Parametric Function Estimates in Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 385-399, September.
    2. Hang Deng & Qiyang Han & Bodhisattva Sen, 2023. "Inference for Local Parameters in Convexity Constrained Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2721-2735, October.
    3. Cécile Durot & Piet Groeneboom & Hendrik P. Lopuhaä, 2013. "Testing equality of functions under monotonicity constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 939-970, December.
    4. Groeneboom,Piet & Jongbloed,Geurt, 2014. "Nonparametric Estimation under Shape Constraints," Cambridge Books, Cambridge University Press, number 9780521864015, November.
    5. Azadbakhsh, Mahdis & Jankowski, Hanna & Gao, Xin, 2014. "Computing confidence intervals for log-concave densities," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 248-264.
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