Statistica Sinica 20 (2010), 613-636
A UNIFIED APPROACH TO
EDGEWORTH EXPANSIONS
FOR A
GENERAL CLASS OF STATISTICS
Bing-Yi Jing and Qiying Wang
Hong Kong University of Science and
Technology and University of Sydney
Abstract: This paper is concerned with Edgeworth
expansions for a general
class of statistics under very weak conditions. Our approach
unifies the treatment for both standardized and studentized
statistics that have been traditionally studied separately under
usually different conditions. These results are then applied to
several special classes of well-known statistics: 
-statistics,
-statistics, and functions of sample means. Special attention is paid to the
studentized statistics. We establish Edgeworth
expansions under very weak or minimal moment conditions.