Consider the density (f(x)=frac{3}{20} 5^{-1 / 2}left(5-x^{2}ight) deltaleft{x ;left(-5^{1 / 2}, 5^{1 / 2}ight)ight}). Prove that (E_{V}^{2}
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Consider the density \(f(x)=\frac{3}{20} 5^{-1 / 2}\left(5-x^{2}ight) \delta\left\{x ;\left(-5^{1 / 2}, 5^{1 / 2}ight)ight\}\). Prove that \(E_{V}^{2} E_{T}^{-2} \simeq 0.864\), which is a lower bound for this asymptotic relative efficiency established by Hodges and Lehmann (1956). Comment on the importance of this lower bound is statistical applications.
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