76. The Kolmogorov test (56) for testing H : F = Fo (Fo continuous) is consistent against any alternative FI Fo, that is, its power against any fixed FI tends to 1 as n -> 00. [The critical value /). = /).n of (56) corresponding to a given a satisfiesj;/). -> K for some K > 0 as n -> 00 . Let a be any value for which FI (

a) Fo (a), and usethefactsthat

(a) IFo

(a) - Tx(a)l:=; supIFo(u) - Tx(u)land

(b) if F= FI , the statistic Tx

(a) has a binomial distribution with success probability p = F)

(a) Fo(a).] [Massey (1950).] Note. For exact power calculations in both the continuous and discrete case, see for example Niederhausen (1981) and GIeser (1985).