...-00662002, version 1 - 22 Jan 2012 We now introduce the so-called α- and β-mixing coefficients. For more details on strong mixing conditions, the reader should refer to the recent survey by C.Bradley =-=[3]-=- or to the monographs [15, 22, 4, 5, 6, 13]. For S ⊂ T a closed subset, we denote by FS the σ-field generated by the random variables {η(s), s ∈ S}. Let S1,S2 ⊂ T be disjoint closed subsets. The α-mix...

...ing coefficient β(S1,S2) can be bounded from above in terms of the extremal coefficient function θ(s1,s2) = θ({s1,s2}), s1,s2 ∈ T. We recall the following basic properties: it always holds θ(s1,s2) ∈ =-=[1,2]-=-; θ(s1,s2) = 2 iff η(s1) and η(s2) are independent; θ(s1,s2) = 1 iff η(s1) = η(s2). Thus the extremal coefficient function gives some insight into the 2-dimensional dependence structure of the max-sta...

... Jan 2012 We now introduce the so-called α- and β-mixing coefficients. For more details on strong mixing conditions, the reader should refer to the recent survey by C.Bradley [3] or to the monographs =-=[15, 22, 4, 5, 6, 13]-=-. For S ⊂ T a closed subset, we denote by FS the σ-field generated by the random variables {η(s), s ∈ S}. Let S1,S2 ⊂ T be disjoint closed subsets. The α-mixing coefficient (or strong mixing coefficie...

...ing coefficient β(S1,S2) can be bounded from above in terms of the extremal coefficient function θ(s1,s2) = θ({s1,s2}), s1,s2 ∈ T. We recall the following basic properties: it always holds θ(s1,s2) ∈ =-=[1,2]-=-; θ(s1,s2) = 2 iff η(s1) and η(s2) are independent; θ(s1,s2) = 1 iff η(s1) = η(s2). Thus the extremal coefficient function gives some insight into the 2-dimensional dependence structure of the max-sta...

...ocedures. Smith [24] noticed that min(η(0) −1 ,η(h) −1 ) as an exponential distribution with mean θ(h) −1 and proposed the estimator ˆθ (2) n (h) = |Λn| ∑ t∈Λn min(η(t)−1 ,η(t+h) −1 ) . Cooley et al. =-=[7]-=- introduced the F-madogram defined by νF(h) = E[|F(η(0))−F(η(h))|] with and show that it satisfies νF(h) = 1θ(h)−1 2θ(h)+1 This suggests the estimator ˆθ (3) n (h) = or equivalently F(y) = exp(−1/y)1{...