Mathematics Theses and Dissertations

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Author: search.filters.author.Moore, Terrence Joseph

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    A Theory of Cramer-Rao Bounds for Constrained Parametric Models
    (2010) Moore, Terrence Joseph; Kedem, Benjamin; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    A simple expression for the Cram'er-Rao bound (CRB) is presented for the scenario of estimating parameters $\theta$ that are required to satisfy a differentiable constraint function $f(\theta)$. A proof of this constrained CRB (CCRB) is provided using the implicit function theorem, and the encompassing theory of the CCRB is proven in a similar manner. This theory includes connecting the CCRB to notions of identifiability of constrained parameters; the linear model under a linear constraint; the constrained maximum likelihood problem, it's asymptotic properties and the method of scoring with constraints; and hypothesis testing. The value of the tools developed in this theory are then presented in the communications context for the convolutive mixture model and the calibrated array model.