Archive for March, 2017

L2 to consistency

E(\hat \theta_n -\mu)^2 \to 0 \implies Pr\left(\big |\hat \theta_n -\mu \big| > \varepsilon\right) \to 0

That L2- convergence implies convergence in probability is a standard result, but I think I have come up with a pretty intuitive exposition as to why it is so. You can read it over at CrossValidated,

http://stats.stackexchange.com/a/270434/28746