Wilks' Theorem states that, under standard regularity conditions, twice the logarithm of the likelihood-ratio test statistic converges, as sample size grows, to a chi-squared distribution whose degrees of freedom equal the difference in the number of free parameters between the two nested models being compared. Named for Samuel S. Wilks, it underlies the widely used likelihood-ratio test and gives the standard asymptotic justification for treating that test statistic as coming from a chi-squared distribution.
Facts
StatementAs the sample size approaches infinity, the distribution of the test statistic -2 log(Lambda) asymptotically approaches the chi-squared distribution under the null hypothesis H0. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Source Wilks' theorem (Wikipedia)
Sources
1. Wilks' theorem (Wikipedia)
Statement of the theorem
as the sample size approaches ∞, the distribution of the test statistic − 2 log(Λ) asymptotically approaches the chi-squared (χ²) distribution under the null hypothesis H₀
References
Wilks, Samuel S. (1938). "The large-sample distribution of the likelihood ratio for testing composite hypotheses". The Annals of Mathematical Statistics.
In Branch: Probability and Statistics, Lead sentence
In statistics, Wilks' theorem offers an asymptotic distribution of the log-likelihood ratio statistic, which can be used to produc
In Group: Mathematical Statistics and Estimation, Lead section
In statistics, Wilks' theorem offers an asymptotic distribution
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