On the Decrease Rate of the Non-Gaussianness of the Sum of Independent Random Variables
<|reference_start|>On the Decrease Rate of the Non-Gaussianness of the Sum of Independent Random Variables: Several proofs of the monotonicity of the non-Gaussianness (divergence with respect to a Gaussian random variable with identical second order statistics) of the sum of n independent and identically distributed (i.i.d.) random variables were published. We give an upper bound on the decrease rate of the non-Gaussianness which is proportional to the inverse of n, for large n. The proof is based on the relationship between non-Gaussianness and minimum mean-square error (MMSE) and causal minimum mean-square error (CMMSE) in the time-continuous Gaussian channel.<|reference_end|>
@article{binia2006on,
    title={On the Decrease Rate of the Non-Gaussianness of the Sum of Independent
  Random Variables},
    author={Jacob Binia},
    journal={arXiv preprint arXiv:cs/0612080},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0612080},
    primaryClass={cs.IT math.IT}
}