Fisher Information Identity and Asymptotic Theory of Hypothesis Tests in Parametric Competing Risks Models under Hybrid Censoring

This technical note presents the core theoretical results of the doctoral dissertation of the author, providing the mathematical foundation for the associated simulation dataset. We establish three main results: (i) The Fisher information identity I(θ₀) = β I_F(θ₀) for parametric competing risks models under hybrid (Type I/II combined) censoring. This identity shows that censoring reduces the available statistical information proportionally to the asymptotic failure fraction β = F(τ*; θ₀). (ii) Asymptotic normality and minimax efficiency of the maximum likelihood estimator (MLE). The MLE attains the Hájek convolution lower bound for any symmetric subconvex loss function. (iii) The Wilks theorem for the Wald (Wₙ), likelihood-ratio (LRₙ), and score (Sₙ) test statistics under composite hypotheses. Under Pitman local alternatives, all three statistics converge to a non-central chi-squared distribution with non-centrality parameter λ* = ξᵀ [R I(θ₀)⁻¹ Rᵀ]⁻¹ ξ. These results justify the theoretical RMSE predictions and power curves tabulated in the companion dataset published in Data in Brief. Explicit formulas for the minimum required sample size are also provided. Keywords: competing risks; hybrid censoring; local asymptotic normality; Fisher information; Wilks theorem; maximum likelihood estimation. MSC 2020: 62G10, 62N05, 62G20, 62F12.

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