On the dependency for asymptotically independent estimates |
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Authors: | Christopher S Withers Saralees Nadarajah |
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Institution: | 1. Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand 2. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK
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Abstract: | Suppose ${\widehat{\theta}_1}$ and ${\widehat{\theta}_2}$ are asymptotically independent non-lattice with a joint second order Edgeworth expansion in n ?1/2. Then the ?? dependency coefficient is $$\alpha \left(\widehat{\theta}_1, \widehat{\theta}_2 \right) = n^{-1/2} C + O \left(n^{-1} \right),$$ where ${C = (4 \pi)^{-1}\exp (-1/2) (\tau^2_1 + \tau^2_2) ^{1/2}}$ for ${\tau_1, \tau_2}$ their joint skewness coefficients. |
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