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

Chi Wing Chu () and Hok Kan Ling ()
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Chi Wing Chu: City University of Hong Kong Kowloon Tong
Hok Kan Ling: Queen’s University Kingston

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2025, vol. 31, issue 3, No 5, 595-630

Abstract: 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.

Keywords: Backward recurrence time; Convexity; Cross-sectional sampling; Current duration data; Log-concavity; Shape constraints; 62G05; 62N02 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10985-025-09658-x

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