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A Comparison of Five Robust Regression Methods with Ordinary Least Squares: Relative Efficiency, Bias and Test of the Null Hypothesis

Description: 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.
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Date: August 2001
Creator: Anderson, Cynthia, 1962-

Disturbing Nature's Beauty: Environmental Aesthetics in a New Ecological Paradigm

Description: An ecological paradigm shift from the "balance of nature" to the "flux of nature" will change the way we aesthetically appreciate nature if we adopt scientific cognitivism-the view that aesthetic appreciation of nature must be informed by scientific knowledge. Aesthetic judgments are subjective, though we talk about aesthetic qualities as if they were objectively inherent in objects, events, or environments. Aesthetic judgments regarding nature are correct insofar as they are part of a community consensus regarding the currently dominant scientific paradigm. Ecological science is grounded in metaphors: nature is a divine order, a machine, an organism, a community, or a cybernetic system. These metaphors stimulate and guide scientific practice, but do not exist independent of a conceptual framework. They are at most useful fictions in terms of how they reflect the values underlying a paradigm. Contemporary ecology is a science driven more by aesthetic than metaphysical considerations. I review concepts in the history of nature aesthetics such as the picturesque, the sublime, disinterestedness, and formalism. I propose an analogy: just as knowledge of art history and theory should inform aesthetic appreciation of art, knowledge of natural history and ecological theory should inform aesthetic appreciation of nature. The "framing problem," is the problem that natural environments are not discrete objects, so knowing what to focus on in an environment is difficult. The "fusion problem" is the problem of how to fuse the sensory aspect of aesthetic appreciation with highly theoretical scientific knowledge. I resolve these two problems by defending a normative version of the theory-laden observation thesis. Positive aesthetics is the view that insofar as nature is untouched by humans, it is always beautiful and never ugly. I defend an amended and updated version of positive aesthetics that is consistent with the central elements of contemporary ecology, and emphasize the heuristic, ...
Date: August 2009
Creator: Simus, Jason Boaz