On the maximum likelihood estimation of a discrete, finite support distribution under left-truncation and competing risks

We prove the classical cause-specific hazard rate estimator is a maximum likelihood estimate (MLE) in a discrete-time, finite support setting. We use an alternative parameterization to simplify the multidimensional constrained optimization problem, which allows for a direct calculus-based solution....

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Bibliographic Details
Published in:Statistics & probability letters 2024-04, Vol.207, p.109973, Article 109973
Main Authors: Lautier, Jackson P., Pozdnyakov, Vladimir, Yan, Jun
Format: Article
Language:English
Subjects:
Asset-backed security
Asset-level disclosures
Convexity
Reg AB II
Reverse hazard rate
Securitization
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Summary:We prove the classical cause-specific hazard rate estimator is a maximum likelihood estimate (MLE) in a discrete-time, finite support setting. We use an alternative parameterization to simplify the multidimensional constrained optimization problem, which allows for a direct calculus-based solution. •We find a direct proof to an open MLE problem via reparameterization.•Restricting the optimization domain to a convex set yields a global maximum.•The sequential solution of the critical point equations confirms uniqueness.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2023.109973