Asymptotic behavior of the maximum from distributions subject to trends in location and scale

Suppose we observe Yjn=μjn+σjnej for 1≤j≤n in R, where {ej} are independent and identical random errors with common distribution function F(x). Let Mn=max1≤j≤nYjn. When the upper tail of F is of power-type, local power type, gamma type and normal type, we give conditions on the growth of the location and scale trends {μjn,σjn} such that for certain constants an and bn>0, bnMn−an converges to one of the three standard extreme value distributions. In each case bn is proportional to the Lp-norm of {σjn} and does not depend on {μjn}. Most importantly, trend in scale is shown to dominate trend in location.