Question
Let \mathbf{p}^0 be the discrete pmf that we wish to test the goodness of fit for an observed sequence of iid samples. Let \widehat{\mathbf{p}} be the MLE upon observing the iid samples.
What is \sqrt{n}\left(\widehat{\mathbf{p}} - \mathbf{p}^0\right)^ T \mathbf{1}?
Note: This is a vector dot product where \left(\widehat{\mathbf{p}} - \mathbf{p}^0\right)^ T is a row vector and \mathbf{1} is the all-ones column vector of appropriate size.
What is \sqrt{n}\left(\widehat{\mathbf{p}} - \mathbf{p}^0\right)^ T \mathbf{1}?
Note: This is a vector dot product where \left(\widehat{\mathbf{p}} - \mathbf{p}^0\right)^ T is a row vector and \mathbf{1} is the all-ones column vector of appropriate size.
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