Statistics Graduate Level Quiz
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CONVERGENCE & LIMIT THEOREMS
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Two correlated estimators measure a treatment mean and a control mean. Their joint limiting distribution is specified in the question.
Suppose n{(μ^T,μ^C)T−(2,1)T}→dN(0,Σ)\sqrt n\{(\widehat\mu_T,\widehat\mu_C)^\mathsf{T}-(2,1)^\mathsf{T}\}\xrightarrow{d}N(0,\Sigma), where Σ=(9334)\Sigma=\begin{pmatrix}9&3\\3&4\end{pmatrix}. For the estimated mean ratio Rn=μ^T/μ^CR_n=\widehat\mu_T/\widehat\mu_C, what is its limiting distribution?
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