Confidence bounds and hypothesis tests for normal distribution coefficients of variation

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.

Subjects

Series Statement

• Research paper FPL-RP -- 638.

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