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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年6月14日

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  • Chi Wing Chu,
  • Hok Kan Ling

摘要

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.