## Abstract

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) |
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Title of host publication | Probability Theory and Extreme Value Theory |

Publisher | De Gruyter Mouton |

Pages | 310-361 |

Number of pages | 52 |

Volume | 2 |

ISBN (Electronic) | 9783110917826 |

ISBN (Print) | 9789067643856 |

State | Published - Jul 11 2011 |

## All Science Journal Classification (ASJC) codes

- General Mathematics