Wald statistic

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Any statistic of the form

W = {g(T)}D−1g(T),

where T is an estimator of a vector parameter θ, g is some vector-valued function, and D is an estimator of the variance–covariance matrix of the vector {g(T)g(θ)}. The statistics are used to test the null hypothesis that g(θ)=0, where 0 is a vector with all entries equal to 0. If T is the maximum likelihood estimator then W has an approximate chi-squared distribution with p degrees of freedom (where p is the number of elements in θ).

Subjects: Probability and Statistics.

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