Information matrix test: Difference between revisions

Revision as of 20:06, 12 September 2018

Revision as of 21:25, 19 February 2019

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: <math>\mathbf{\Delta}(\mathbf{\theta}) = \sum_{i=1}^n \left[ \frac{\partial^2 \ell(\mathbf{\theta}) }{ \partial \mathbf{\theta} \, \partial \mathbf{\theta}^{\mathsf{T}} } + \frac{\partial \ell(\mathbf{\theta}) }{ \partial \mathbf{\theta} } \frac{\partial \ell (\mathbf{\theta}) }{ \partial \mathbf{\theta} } \right]</math>

where <math>\mathbf{\Delta} (\mathbf{\theta})</math> is an <math>(r \times r) </math> [[random matrix]], where <math>r</math> is the number of parameters. White showed that the elements of <math>n^{-1/2} \mathbf{\Delta} ( \mathbf{\hat{\theta}} )</math>, where <math>\mathbf{\hat{\theta}}</math> is the MLE, are asymptotically [[Normal distribution|normally distributed]] with zero means when the model is correctly specified.<ref>{{cite book |first=L. G. |last=Godfrey |title=Misspecification Tests in Econometrics |___locationpublisher=New York |publisher=[[Cambridge University Press]] |year=1988 |isbn=0-521-26616-5 |pages=35–37 }}</ref>

== References ==