No abstract

and three anonymous referees for suggestions that led to improved content and exposition. 'The International Olympic Committee, for instance, selected six cities as "finalists" for the 1996 Summer Olympics: Belgrade, Manchester, Toronto, Melbourne, Athens, and Atlanta. 2Atlanta won the bid for the 1996 Olympics. MARCH 1993 Theorem 1 characterizes expected revenue for the entire continuum of equilibria that can arise in n > 2-player all-pay auctions with arbitrary valuations of the prize. This is in contrast to the results of Ellingsen (1991), Hillman (1988), Hillman and Riley (1989), and Hillman and Dov Samet (1987), among others, which are valid only for a subset of possible equilibria.

Tail index estimation depends for its accuracy on a precise choice of the sample fraction, i.e., the number of extreme order statistics on which the estimation is based. A complete solution to the sample fraction selection is given by means of a two-step subsample bootstrap method. This method adaptively determines the sample fraction that minimizes the asymptotic mean-squared error. Unlike previous methods, prior knowledge of the second-order parameter is not required. In addition, we are able to dispense with the need for a prior estimate of the tail index which already converges roughly at the optimal rate. The only arbitrary choice of parameters is the number of Monte Carlo replications. Academic PressAMS 1991 subject classifications: 62G32, 62F40.

} are i.i.d. IWt-valued random pairs. A special case of interest is when { Y,,} is derived from a first order ARCH process. Parameters of the limit law are exhibited; some are hard to calculate explicitly but easy to simulate.