A theory of matrix-valued functions from the matricial Smirnov class Nn (D) is systematically developed. In particular, the maximum principle of V.I.Smirnov, inner-outer factorization, the Smirnov-Beurling characterization of outer functions and an analogue of Frostman’s theorem are presented for matrix-valued functions from the Smirnov class Nn (D). We also consider a family Fλ = F − λI of fun...

G08CDF also returns the standardized statistic Z 1⁄4 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n1 þ n2 n1n2 r D, where D may be Dn1;n2 , D þ n1;n2 or D n1;n2 depending on the choice of the alternative hypothesis. The distribution of this statistic converges asymptotically to a distribution given by Smirnov as n1 and n2 increase; see Feller (1948), Kendall and Stuart (1973), Kim and Jenri...

1 Some Basic Theory 1 1.1 Consistency and Unbiasedness at a Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Kolmogorov–Smirnov Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Order Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Proof of the Kolmogorov–Smirnov Theorem . . ....