Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The Berry-Esseen theorem is a quantitative version of the central limit theorem which sets an upper bound on deviation from normality based on the sample size $n$. The equation for identically distributed random variables is $sup|F_n(x)-\phi(x)| \le C_0*\frac{\rho}{\sigma^3*\sqrt{n}}$ where $F_n$ is the centered normalized cdf of your sample and $\phi$ is the standard normal cdf. Or at least, that's my understand of it.

I'm confused how this equation makes sense in the context of symmetric equations. When the skewness $\rho$ is zero the right side of the equation is zero. Since it should be an upper bound, that implies that the supremum of the deviation from normality (left side of the equation) is zero and not dependent on the sample size $n$.

Help? Am I misunderstanding the purpose of the equation?

share|improve this question
add comment

1 Answer

up vote 3 down vote accepted

The $\rho$ in the Berry-Essen theorem is defined as $\rho =\mathbb{E}\left(|X|^3\right)$. It is explicitly positive assuming $\sigma>0$. In other words, you may be conflating $\rho$ as the correlation coefficient, which it is not.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.