likelihood ratio test

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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 θ̂R and θ̂U, the maximum likelihood estimators of θ obtained with and without restrictions:

λ = L(θ̂R)/L(θ̂U).

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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