Notes 10 : Asymptotic Sample Complexity 2 LEM 10

Ξ = {ΞX , . . .}, be a sequence of i.i.d. samples generated by a CFN model (T ,P). A sequence of estimators {T̂k}k≥0 of T , where T̂k is based on k samples, has asymptotic sample complexity (ASC) at confidence level δ (at most) k0 if for all k ≥ k0 the probability that T̂k = T is at least δ. Typically, the ASC is expressed as an asymptotic expression of structural parameters of the model such as the number of leaves n, the shortest branch length f , or the diameter of the tree.