I'm looking to bound the error of the CLT approximation. Would like the error to decrease faster than sqrt(n). Does anyone know of such results?
I'm happy to assume more structure on my random variable, within limits. Thanks bros.
You can do better by approximating by skew-normal distribution, see https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1D56C58B6B1607F4E78AB7CBCB2A434/S0021900200011360a.pdf/improved_approximation_of_the_sum_of_random_vectors_by_the_skew_normal_distribution.pdf
You can assume your random variable is Gasssian. Then error of CLT approximation is 0. Otherwise you cannot do faster.
Correction. I guess if the 3rd order centralized moment was zero then you could prove your convergence was faster. Similarly if 4th, etc higher order centralized moments were zero you could prove faster convergence.
You can assume your random variable is Gasssian. Then error of CLT approximation is 0. Otherwise you cannot do faster.Correction. I guess if the 3rd order centralized moment was zero then you could prove your convergence was faster. Similarly if 4th, etc higher order centralized moments were zero you could prove faster convergence.
it's the skewness
You can do better by approximating by skew-normal distribution, see https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A1D56C58B6B1607F4E78AB7CBCB2A434/S0021900200011360a.pdf/improved_approximation_of_the_sum_of_random_vectors_by_the_skew_normal_distribution.pdf
Thanks for this. Looks good.