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The asymptotic distribution of the likelihood ratio in the regular case. (English) Zbl 0663.62030

It may not be generally realized that the asymptotic distribution of the likelihood ratio, when a null hypothesis imposing two restrictions on the parameters is true (and the usual regularity conditions hold), is the uniform. Extending this result to the asymptotic null distribution of the likelihood ratio in the general case, assuming regularity, allows an interesting interpretation of that distribution in terms of products of indepenent uniforms and, in some cases, other functions of uniforms. A corresponding interpretation when the null hypothesis is false is also given.

MSC:

62E20 Asymptotic distribution theory in statistics
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References:

[1] Wilks S. S., Mathematical Statistics (1962) · Zbl 0173.45805
[2] Strawderman, W. E. 1983.Encyclopedia of Statistical Sciences, Edited by: Kotz, S. and Johnson, N. L. Volume 4, 647–650. New York: Wiley.
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[5] DOI: 10.1090/S0002-9947-1943-0012401-3 · doi:10.1090/S0002-9947-1943-0012401-3
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