“likelihood ratio test”的概念、定义、翻译、参考文献-科学参考

likelihood ratio test

Mathematics

A sophisticated hypothesis test which compares the likelihood of the observed value happening for different possible values of the parameter under investigation. In its simplest form, the comparison is between two possible values, but more generally the alternatives are ranges of the parameter value and the comparison is for maximum likelihoods in the interval.

Economics

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 θ‎^̂^R and θ‎^̂^U, the maximum likelihood estimators of θ‎ obtained with and without restrictions: λ‎ = L(θ‎^̂^R)/L(θ‎^̂^U). Under certain regularity conditions and under the null hypothesis the quantity −2ln (λ‎) has asymptotically chi-square distribution, with degrees of freedom equal to the number of restrictions.

单词	likelihood ratio test
释义	likelihood ratio test Mathematics A sophisticated hypothesis test which compares the likelihood of the observed value happening for different possible values of the parameter under investigation. In its simplest form, the comparison is between two possible values, but more generally the alternatives are ranges of the parameter value and the comparison is for maximum likelihoods in the interval. Economics 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 θ‎^̂^R and θ‎^̂^U, the maximum likelihood estimators of θ‎ obtained with and without restrictions: λ‎ = L(θ‎^̂^R)/L(θ‎^̂^U). Under certain regularity conditions and under the null hypothesis the quantity −2ln (λ‎) has asymptotically chi-square distribution, with degrees of freedom equal to the number of restrictions.
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