Two-sample U-statistic processes for long-range dependent data. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Dehling, H.; Rooch, A.; Wendler, M.
• Is Part Of: Statistics. Volume 51:Issue 1(2017)
• Page Start: 84
• Page End: 104
• Publication Date: 2017-01-02
• Subjects: U-statistic processes -- long-range dependence -- Hermite polynomials -- empirical processes -- change-point problems -- non-central limit theorems; 60F17 -- 62G30 -- 62M10; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2016.1270542
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: Motivated by some common change-point tests, we investigate the asymptotic distribution of the U -statistic processU n ( t ) = ∑ i = 1 [ n t ] ∑ j = [ n t ] + 1 n h ( X i, X j ), 0 ≤ t ≤ 1, when the underlying data are long-range dependent. We present two approaches, one based on an expansion of the kernelh ( x, y ) into Hermite polynomials, the other based on an empirical process representation of the U -statistic. Together, the two approaches cover a wide range of kernels, including all kernels commonly used in applications.