0
$\begingroup$

Assume $X_i$ has zero mean and unit variance. Define $S_n = \sum_{i=1}^n X_i$.

In the law of large numbers, the quantity $S_n/n$ means sample mean.

In the central limit theorem, the quantity $S_n/\sqrt{n}$ means normalized sample mean to have zero mean and unit variance.

I was wondering what the meaning of the quantity $S_n/\sqrt{n\log\log n}$ in the law of iterated logarithm is?

Thanks!

  • 0
    What do you mean when you say "$S_n/n$ means sample mean" and "$S_n/\sqrt{n}$ means normalized sample mean..."?2012-10-18
  • 0
    They are sample mean and normalized sample mean for the sample $(X_1, \dots, X_n)$.2012-10-18
  • 0
    Does the normalized sample mean have a special meaning?2012-10-18
  • 0
    normalized to have mean zero and variance 1.2012-10-18

1 Answers 1