UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

More information is available at Theses and Dissertations at University of Maryland Libraries.

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Author: search.filters.author.Moore, Terrence JosephSubject: search.filters.subject.constraints

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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.