THE TAIL ESTIMATION FOR THE DISTRIBUTION OF THE SUPREMA OF A P-BRIDGE

Let X_1,X_2,…be a sequence of independent random vectors which take values in IR~2 and X_i～P.By the projection pursuit (PP) method,we canconstruct PP type Kolmogrov-Smirnov statistics:K_n=(?) 1/n~(1/2)|sum from i=1 to n(I_|a~rX_(?)(?)t|-P(a~rX_1(?)t))|,where I_(·]) is the indicator function of the set ·] and P is a probability distribution.The limit distribution of K_n is the distribution for the suprema of a P-bridgewhose index is the set of all half spaces in IR~2.Let{W_p(0,(?)])∶(?)∈0,1]~2} be atwo parameter Brownish bridge.The main result of this paper is(?)for all λ,provided P is the uniform distribution on 0,k_1]×0,k_2],0

THE TAIL ESTIMATION FOR THE DISTRIBUTION OF THE SUPREMA OF A P-BRIDGE