Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 1984, Volume 52, Issue 4

Hypothesis Testing in Linear Models when the Error Covariance Matrix is Nonscalar<827:HTILMW>2.0.CO;2-U
p. 827-842

Thomas J. Rothenberg

Stochastic expansions are developed for the Lagrange multiplier, likelihood ratio, and Wald statistics for testing regression coefficients in the normal linear model with unknown error covariance matrix. Under suitable regularity conditions, the likelihood ratio statistic is found to be approximately the average of the other two. Critical values are calculated so that the three tests have approximately the same size. The second-order approximate local power functions indicate that, when the null hypothesis is one dimensional, all three tests are equally powerful. When the hypothesis is multidimensional, the power functions differ; no one of the tests is uniformly more powerful than the others.

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