## Quick Reference

One of the three tests of restrictions (along with the Lagrange multiplier test and the Wald test) on an unknown parameter, or a vector of unknown parameters, *θ*, based on maximum likelihood estimation of *θ*. The test statistic is the ratio of the likelihood functions evaluated at *θ̂*^{R} and *θ̂*^{U}, the maximum likelihood estimators of *θ* obtained with and without restrictions:

*λ* = *L(θ̂*^{R})/*L(θ̂*^{U}).

Under certain regularity conditions and under the null hypothesis the distribution of −2ln (*λ*) in a large sample is chi-square, with degrees of freedom equal to the number of restrictions.

*Subjects:*
Economics — Mathematics.

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