Entropy and Random Vectors |
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Authors: | Oliver Johnson Yurii Suhov |
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Institution: | (1) Statistical Laboratory, CMS, Wilberforce Road, Cambridge, CB3 DWB, United Kingdom |
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Abstract: | Barron(1) produced a proof of the Central Limit Theorem for real-valued IID random variables, in the sense of convergence in relative entropy. Here, we establish a similar result for independent real-valued random vectors, not necessarily identically distributed. The main developments required are a generalisation of De Bruijn's identity, and various inequalities proposed in ref. 2. |
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Keywords: | normal convergence entropy Fisher information |
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