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A Reminder of the Fallibility of the Wald Statistic: Likelihood Explanation
The American Statistician
Vol. 54, No. 1 (Feb., 2000), pp. 54-56
Stable URL: http://www.jstor.org/stable/2685612
Page Count: 3
You can always find the topics here!Topics: Statistics, Statistical variance, Approximation, Confidence interval, Maximum likelihood estimators, Ratio test, Maximum likelihood estimation, Mathematical independent variables
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The Wald statistic is one of the most commonly used tools in applied statistics, so it is sobering to read Fears, Benichou, and Gail's recent reminder of its fallibility. What makes their example particularly relevant is the fact that the problem is manifest in a simple normal random effects model on a balanced dataset for a seemingly harmless parameter, while, in practice, one tends to rely on the Wald test in complicated or nonnormal models where there are no exact tests to serve as a gold standard. This article explains the failure of the Wald test via the profile likelihood functions, which graphically look decidedly nonnormal. The methodology used to derive the profile likelihood and the discussion of this example could be instructive for a senior or beginning graduate class in theory of statistics.
The American Statistician © 2000 American Statistical Association