Let D((0 l] 2 ) denote the space of all functions on (0,l] 2 with no discontinuities of the second kind. We prove weak invariance principles in the space D((0,l] 2 ) for processes of the form ∫h(H n+m (t))dF n (t), m, n ≤ 1, where F n and G m are two independent empirical distribution functions of independent, identically distributed sequences of random variables, H n+m = (n+m+I) -1 (nF n + mG m ), and where h belongs to a certain class of functions on the open unit interval. The appropriate topology in D(((0,l] 2 ) is given by uniform convergence on compact sets. This type of processes is central in nonparametric statistics having applications to two-sample linear rank statistics and signed rank statistics.
|Original language||English (US)|
|Title of host publication||Probability Theory and Extreme Value Theory|
|Publisher||De Gruyter Mouton|
|Number of pages||52|
|State||Published - Jul 11 2011|
All Science Journal Classification (ASJC) codes