The likelihood ratio test is a hypothesis test. It allows to test general hypotheses concerning the parameters of interest of a parametric family as well as to test two different models built on the same data. The main idea of this test is the following: compute the probability of observing the data under the null hypothesis H 0 and under the alternative hypothesis using the likelihood function.
HISTORY
It is Neyman, Jerzy and Pearson, Egon Sharpe (1928) who came up with the idea of using the likelihood ratio statistic to test hypotheses. Wald, Abraham (1941) generalized the likelihood ratio test to more complicated hypotheses. The asymptotic results on the distribution of this statistic (subject to certain regularity conditions) were first presented by Wilks, Samuel Stanley (1962).
MATHEMATICAL ASPECTS
In the likelihood ratio test, the null hypothesis is rejected if the likelihood under the alternative hypothesisis significantly larger than the likelihood under the...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
REFERENCES
Cox, D.R., Hinkley, D.V.: Theoretical Statistics. Chapman & Hall, London (1973)
Edwards, A.W.F.: Likelihood. An account of the statistical concept of likelihood and its application to scientific inference. Cambridge University Press, Cambridge (1972)
Kendall, M.G., Steward, A.: The Advanced Theory of Statistics, vol. 2. Griffin, London (1967)
Neyman, J., Pearson, E.S.: On the use and interpretation of certain test criteria for purposes of statistical inference, Parts I and II. Biometrika 20A, 175–240, 263–294 (1928)
Wald, A.: Asymptotically Most Powerful Tests of Statistical Hypotheses. Ann. Math. Stat. 12, 1–19 (1941)
Wald, A.: Some Examples of Asymptotically Most Powerful Tests. Ann. Math. Stat. 12, 396–408 (1941)
Wilks, S.S.: Mathematical Statistics. Wiley, New York (1962)
Rights and permissions
Copyright information
© 2008 Springer-Verlag
About this entry
Cite this entry
(2008). Likelihood Ratio Test. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_233
Download citation
DOI: https://doi.org/10.1007/978-0-387-32833-1_233
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-31742-7
Online ISBN: 978-0-387-32833-1
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering