Мақола

A Bernstein–von Mises Theorem for Parametric Competing Risks Under Hybrid Censoring

N. S. NurmukhamedovaDepartment of Econometrics and Economic Modeling, National University of Uzbekistan Named After Mirzo Ulugbek, Universitetskaya Str. 4, Tashkent 100174, UzbekistanGuzal AbdujalilovaDepartment of Econometrics and Economic Modeling, National University of Uzbekistan Named After Mirzo Ulugbek, Universitetskaya Str. 4, Tashkent 100174, UzbekistanMirkamol BerdimuratovDepartment of Computational Mathematics and Information Systems, National University of Uzbekistan Named After Mirzo Ulugbek, Universitetskaya Str. 4, Tashkent 100174, UzbekistanNargiza BoltaevaDepartment of Econometrics and Economic Modeling, National University of Uzbekistan Named After Mirzo Ulugbek, Universitetskaya Str. 4, Tashkent 100174, UzbekistanGulhayo XalilovaDepartment of Probability Theory and Mathematical Statistics, National University of Uzbekistan Named After Mirzo Ulugbek, Universitetskaya Str. 4, Tashkent 100174, UzbekistanUmidjon YODGOROVDepartment of Computer Linguistics and Digital Technologies, Alisher Navoiy Tashkent State University of the Uzbek Language and Literature, Tashkent 100070, UzbekistanDilsuz KhamraevaDepartment of Engineering and Economics, ZARMED University, Bukhara Campus, Qayum Murtazoyev Str. 13A, Bukhara 200117, UzbekistanDilafruz KhamraevaDepartment of Engineering and Economics, ZARMED University, Bukhara Campus, Qayum Murtazoyev Str. 13A, Bukhara 200117, Uzbekistan

2026en

ABI

Аннотация

We establish a Bernstein–von Mises (BvM) theorem for parametric competing-risks models under hybrid Type-I censoring, where observation stops at the random time τn=min(X(r),T0). Using the counting-process martingale framework, we first prove the local asymptotic normality (LAN) of the model and identify the limiting Fisher information as a block-diagonal matrix composed of operational (τ∗-truncated) cause-specific informations. Unlike previous work, we derive the testing-function (Hellinger-affinity) condition required for posterior tail control from the standard regularity assumptions rather than imposing it as an extra hypothesis. The posterior distribution of n(θ−θ^n) is shown to converge in total variation to a Gaussian law with covariance I(θ0)−1 for every prior positive and continuous at θ0. The convergence rate is OP((logn)3/2n−1/2); a fourth-order smoothness condition removes the logarithmic factor. The abstract conditions are verified for the exponential, Weibull, and Gompertz families, and a simulation study corroborates the asymptotic approximation and the nominal coverage of Bayesian credible sets.

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DOI: 10.3390/math14183277

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