Let $X_1, X_2... X_n$ be a iid sample of size $n$ from some distribution. How can I check if the distribution of these $X_i$ is subgaussian? Is there some statistical test I can apply?
My thought is that a distribution is subgaussian if it's tails are bounded by some gaussian, but in practice I can always find some gaussian distribution whose tails dominate those of my finite sample of size $n$.