In this paper we obtain asymptotic representations of several variance estimators of U-statistics and study their effects for studentizations via Edgeworth expansions. Jackknife, unbiased and Sen's variance estimators are investigated up to the order op(n-1). Substituting these estimators to studentized U-statistics, the Edgeworth expansions with remainder term o(n-1) are established and inverting the expansions, the effects on confidence intervals are discussed theoretically. We also show that Hinkley's corrected jackknife variance estimator is asymptotically equivalent to the unbiased variance estimator up to the order op(n-1).
|Number of pages||20|
|Journal||Annals of the Institute of Statistical Mathematics|
|Publication status||Published - Jan 1 1998|
All Science Journal Classification (ASJC) codes
- Statistics and Probability