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Abstract
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 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 Cramer 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,
n-consistent estimators,
efficient likelihood estimators,
Cramer conditions,
quadratic mean differentiability,
likelihood ratio test,
Wald test,
Rao test,
asymptotics,
confidence internals,
Newton-Raphson method
Citation
Verrill, Steve P.; Johnson, Richard A. 2007. Confidence bounds and hypothesis tests for normal distribution coefficients of variation. Research Paper FPL-RP-638. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 57 pages
