Jennings-Shaffer, Chris, Skinner, Dane R. and Waymire, Edward C. (2018). WHEN FOURTH MOMENTS ARE ENOUGH. Rocky Mt. J. Math., 48 (6). S. 1917 - 1925. TEMPE: ROCKY MT MATH CONSORTIUM. ISSN 1945-3795
Full text not available from this repository.Abstract
This note concerns a somewhat innocent question motivated by an observation concerning the use of Chebyshev bounds on sample estimates of p in the binomial distribution with parameters n, p, namely, what moment order produces the best Chebyshev estimate of p ? If S-n(p) has a binomial distribution with parameters n, p, then it is readily observed that argmax(0 <= p <= 1) ESn2 (p) = argmax(0 <= p <= 1) np(1 - p) = 1/2, and ESn2(1/2) = n/4. Bhattacharya [2] observed that, while the second moment Chebyshev sample size for a 95 percent confidence estimate within +/- 5 percentage points is n = 2000, the fourth moment yields the substantially reduced polling requirement of n = 775. Why stop at the fourth moment ? Is the argmax achieved at p = 1/2 for higher order moments, and, if so, does it help in computing ESn2m (1/2)? As captured by the title of this note, answers to these questions lead to a simple rule of thumb for the best choice of moments in terms of an effective sample size for Chebyshev concentration inequalities.
Item Type: | Journal Article | ||||||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-201119 | ||||||||||||||||
DOI: | 10.1216/RMJ-2018-48-6-1917 | ||||||||||||||||
Journal or Publication Title: | Rocky Mt. J. Math. | ||||||||||||||||
Volume: | 48 | ||||||||||||||||
Number: | 6 | ||||||||||||||||
Page Range: | S. 1917 - 1925 | ||||||||||||||||
Date: | 2018 | ||||||||||||||||
Publisher: | ROCKY MT MATH CONSORTIUM | ||||||||||||||||
Place of Publication: | TEMPE | ||||||||||||||||
ISSN: | 1945-3795 | ||||||||||||||||
Language: | English | ||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||
Subjects: | no entry | ||||||||||||||||
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Refereed: | Yes | ||||||||||||||||
URI: | http://kups.ub.uni-koeln.de/id/eprint/20111 |
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