Confidence bounds and hypothesis tests for normal distribution coefficients of variation
By: Steve P. Verril, Richard A. Johnson.
Contributors: Johnson, Richard A.; Forest Products Laboratory (U.S.)
Series: Research paper FPL-RP -- 638.
Publisher: USDA, Forest Service, Forest Products Laboratory
Published: 2007
Place of publication: Madison, WI
Language: eng
Number of pages: 57
Subjects: Statistical hypothesis testing -- Asymptotic theory.; Confidence intervals.
Description: For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations. To develop these confidence bounds and test, we first establish that estimators based on Newton steps from [the square root of n]-consistent estimators may be used in place of efficient solutions of the likelihood equations in likelihood ratio, Wald, and Rao tests. Taking a quadratic mean differentiability approach, Lehmann and Romano have outlined proofs of similar results. We take a Cramér condition approach and make the conditions and their use explicit. Keywords: coefficient of variation, signal to noise ratio, risk to return ratio, one-step Newton estimators, Newton's method, [the square root of n]-consistent estimators, efficient likelihood estimators, Cramér conditions, quadratic mean differentiability, likelihood ratio test, Wald test, Rao test, asymptotics.
Notes: Cover title.

"September 2007"--P. [2] of cover.

Includes bibliographical references (p. 11-12).

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