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Thesis (M.S.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (February 5, 2007) Includes bibliographical references.

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 201-205).

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 171-177).

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 49-50).

This thesis mainly proposes a new method to design Hinf Loop Shaping Robust Controller by choosing Weighting Function. In the paper, the author first introduces the concept of SISO Loop Shaping design. It utilizes Small Gain Theorem to achieve robust stability of the system and develops the relationship of Open Loop Transfer Function(L) to Robust Performance and to Robust Stability of the system.. These concepts can be extended to Hinf Loop Shaping method. As to Hinf loop shaping method, the author first introduces the problem of Robust Stability under the framework of Coprime Factor and the theory of Hinf Loop Shaping, and then discusses the relationship between stability margin and the different pole-zero system. Generally speaking, the control theories of the Loop Shaping are mainly used for making appropriate adjustments between the stability and performance of the system. Because the system can conform to the performance requirement through the choice of Weighting Function, the author proposes a new method toward MIMO system to design Hinf Loop Shaping Controller by choosing Weighting Function under the framework of Hinf Loop Shaping. Moreover, at the end of the paper,the author compares the result of the new method with that of the literature.

A Monte Carlo simulation was used to generate data for a comparison of five robust regression estimation methods with ordinary least squares (OLS) under 36 different outlier data configurations. Two of the robust estimators, Least Absolute Value (LAV) estimation and MM estimation, are commercially available. Three authormodified variations on MM were also included (MM1, MM2, and MM3). Design parameters that were varied include sample size (n=60 and n=180), number of independent predictor variables (2, 3 and 6), outlier density (0%, 5% and 15%) and outlier location (2x,2y s, 8x8y s, 4x,8y s and 8x,4y s). Criteria on which the regression methods were measured are relative efficiency, bias and a test of the null hypothesis. Results indicated that MM2 was the best performing robust estimator on relative efficiency. The best performing estimator on bias was MM1. The best performing regression method on the test of the null hypothesis was MM2. Overall, the MM-type robust regression methods outperformed OLS and LAV on relative efficiency, bias, and the test of the null hypothesis.

The classical parametric estimation approach, maximum likelihood, while providing maximally efficient estimators at the correct model, lacks robustness. As a modification of maximum likelihood, Huber (1964) introduced M-estimators, which are very general but often ad hoc. Basu et al. (1998) developed a family of density-based divergences, many of which exhibit robustness. It turns out that maximum likelihood is a special case of this general class of divergence functions, which are indexed by a parameter alpha. Basu noted that only values of alpha in the [0,1] range were of interest -- with alpha = 0 giving the maximum likelihood solution and alpha = 1 the L2E solution (Scott, 2001). As alpha increases, there is a clear tradeoff between increasing robustness and decreasing efficiency. This thesis develops a family of robust location and scale estimators by applying Basu's alpha-divergence function to a multivariate partial density component model (Scott, 2004). The usefulness of alpha values greater than 1 will be explored, and the new estimator will be applied to simulated cases and applications in parametric density estimation and regression.

Implemented robust regressio technology in portfolio optimization. Constructed optimized portfolio based on robust regression estimations. Compared the portfolio performance with optimized portfolio which is based on ordinary least square estimation.