A point-process approach to almost-sure behaviour of record values and order statistics

Point-process and other techniques are used to make a comprehensive investigation of the almost-sure behaviour of partial maxima (the rth largest among a sample of n i.i.d. random variables), partial record values , and differences and quotients involving them. In particular, the authors obtain characterizations of such asymptotic properties as lim a.s. for some finite constant c, or a.s. for some constant c in , which tells us, in various ways, how quickly the sequences increase. These characterizations take the form of integral conditions on the tail of F, which furthermore characterize such properties as stability and relative stability of the sequence of maxima. They also develop their relation to the large-sample behavior of trimmed sums, and discuss some statistical applications.