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Activity Number:
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210
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Type:
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Contributed
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Date/Time:
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Monday, August 7, 2006 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Survey Research Methods
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| Abstract - #307548 |
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Title:
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How Bad Could Your Data Be? Variance Maximization
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Author(s):
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Jeffrey Stuart*+
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Companies:
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Pacific Lutheran University
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Address:
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Mathematics Department, Tacoma, WA, 98447,
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Keywords:
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variance maximization
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Abstract:
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For a finite, simple random sample from a closed, bounded subset S of real n-space, how large can the variance be? We show that the answer is largely determined by the convex hull of S, and that each maximum variance subset of S is comprised of certain extreme points of the convex hull. An alternative formulation in terms of sets of end points of diameters of S is presented and used in conjunction with circumscribing spheres to bound the maximum variance. Results depend on whether the sample size is even or odd. Variance maximization has application to information theory. This work was motivated by a question originally posed to the AP Statistics newsgroup. The mathematical content is accessible to those with a semester of advanced calculus and several lectures on convex analysis.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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