Weak Invariance Principles for Regression Rank Statistics

Abstract

Weak invariance principles are proved for regression rank statistics. As a consequence limit theorems for max- and L _p -functionals of partial sums of vectors of simple linear rank statistics are obtained. The results are useful in change point analysis, particularly in justification of application of permutation arguments, see Antoch and Hušková [Antoch, J.; Hušková, M. Detection of Structural Changes in Regression. Tatra Mountains Publications, 2003, 26, 1–15] and Hušková and Picek [Hušková, M.; Picek, J. M-tests for detection of structural changes in regression. In Statistical Data Analysis Based on the L ₁-Norm and Related Methods; Dodge, Y., Ed.; Birhäuser: Basel, 2002; 213–229]. The results of Hušková [Hušková, M. Limit theorems for rank statistics. Statist. Probab. Letters 1997, 32, 45–55] are generalized.

Key Words:

• Simple linear rank statistics
• Weak invariance principle
• Change point analysis

2000 Mathematical Subject Classification:

• 62G20
• 62E20
• 60F17

Acknowledgment

The work was supported by grants GAČR 201/03/0945 and MSM 113200008.

Notes

Recommended by T. L. Lai