Likelihood Ratio
المؤلف:
Feller, W.
المصدر:
An Introduction to Probability Theory and Its Applications, Vol. 2, 3rd ed. New York: Wiley
الجزء والصفحة:
...
2-5-2021
1983
Likelihood Ratio
A quantity used to test nested hypotheses. Let 
be a nested hypothesis with 
degrees of freedom within 
(which has 
degrees of freedom), then calculate the maximum likelihood of a given outcome, first given 
, then given 
. Then
Comparison of 
to the critical value of the chi-squared distribution with 
degrees of freedom then gives the significance of the increase in likelihood.
The term likelihood ratio is also used (especially in medicine) to test nonnested complementary hypotheses as follows,
REFERENCES:
Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 2, 3rd ed. New York: Wiley, pp. 211-212, 1971.
Hoel, P. G. "Likelihood Ratio Tests." §9.1.4 in Introduction to Mathematical Statistics, 3rd ed. New York: Wiley, pp. 220-228, 1962.
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