Non-uniform Berry–Esseen bounds for martingales with applications to statistical estimation. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Fan, X.; Grama, I.; Liu, Q.
• Is Part Of: Statistics. Volume 51:Issue 1(2017)
• Page Start: 105
• Page End: 122
• Publication Date: 2017-01-02
• Subjects: Non-uniform Berry–Esseen bound -- Cramér large deviations -- exponential inequality -- linear regressions -- self-normalized large deviations; 60G42 -- 60F05 -- 60F10 -- 60E15 -- 62E20 -- 62J05; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2016.1270007
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: We establish non-uniform Berry–Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cramér type large deviations for moderate x 's, and are of exponential decay rate as de la Peña's inequality whenx → ∞ . Statistical applications associated with linear regressions and self-normalized large deviations are also provided.