Validity of the LRT under covariate-dependent censoring

Establish the asymptotic validity of the likelihood ratio test for unobserved heterogeneity in censored Weibull duration models when censoring depends on covariates.

Background

The paper compares its EM test with the likelihood ratio test (LRT) for detecting unobserved heterogeneity in censored Weibull duration models. The asymptotic null distribution of the LRT had previously been formally established only for fixed censoring and random censoring, whereas the paper allows censoring to depend arbitrarily on observed covariates, subject to conditional independence between duration and censoring given those covariates.

Because the LRT’s asymptotic theory is not established in the covariate-dependent setting, the authors nevertheless apply the same weighted-bootstrap procedure used under covariate-independent censoring in their simulations. They explicitly identify the validity of the LRT in this broader censoring regime as unresolved.

References

Unlike the IM and LM tests, whose $\chi2$ asymptotic null distributions follow from Assumptions \ref{assn1}--\ref{assn3} regardless of whether censoring depends on ${X}_t$, the LRT's asymptotic null distribution has been formally established by \citet{chowhite10joe} only under fixed or random censoring. Its validity under covariate-dependent censoring is, at present, an open question.

— Testing for Unobserved Heterogeneity in Censored Duration Models: EM Approach  (2609.36824 - Kasahara et al., 29 Sep 2026) in Section 5.2, subsection “Covariate-dependent censoring”