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Full-Text Articles in Probability
Statistical Roles Of The G-Expectation Framework In Model Uncertainty: The Semi-G-Structure As A Stepping Stone, Yifan Li
Electronic Thesis and Dissertation Repository
The G-expectation framework is a generalization of the classical probability system based on the sublinear expectation to deal with phenomena that cannot be described by a single probabilistic model. These phenomena are closely related to the long-existing concern about model uncertainty in statistics. However, the distributions and independence in the G-framework are quite different from the classical setup. These distinctions bring difficulty when applying the idea of this framework to general statistical practice. Therefore, a fundamental and unavoidable problem is how to better understand G-version concepts from a statistical perspective.
To explore this problem, this thesis establishes a new substructure …
New Developments On The Estimability And The Estimation Of Phase-Type Actuarial Models, Cong Nie
New Developments On The Estimability And The Estimation Of Phase-Type Actuarial Models, Cong Nie
Electronic Thesis and Dissertation Repository
This thesis studies the estimability and the estimation methods for two models based on Markov processes: the phase-type aging model (PTAM), which models the human aging process, and the discrete multivariate phase-type model (DMPTM), which can be used to model multivariate insurance claim processes.
The principal contributions of this thesis can be categorized into two areas. First, an objective measure of estimability is proposed to quantify estimability in the context of statistical models. Existing methods for assessing estimability require the subjective specification of thresholds, which potentially limits their usefulness. Unlike these methods, the proposed measure of estimability is objective. In …