Convergence rate

Using Chernoff's theorem :

• $Prob[\vert\hat{V_{N}}-\bar{v}\vert\geq\gamma]\leq 2e^{-2N\gamma^{2}}$
• $Prob[\hat{V_{N}}>(1+\gamma)\bar{v}]\leq e^{-N\bar{v}\gamma^{2}/3}$
• $Prob[\hat{V_{N}}<(1-\gamma)\bar{v}]\leq e^{-N\bar{v}\gamma^{2}/2}$

Note that convergence rate is exponential in the sample size.