Asymptotic Expansions for the Power of Distribution Free Tests in the One-Sample Problem

The Edgeworth Expansion for U-Statistics of Degree Two

“…We stress the fact that previous results on Edgeworth expansions for U-statistics would fail in this case because UN has a pure lattice distribution. Edgeworth expansions for one-sample rank statistics were obtained in Albers, Bickel and van Zwet (1976) by a completely different method.…”

A method for obtaining asymptotic expansions under alternatives based on the properties of the likelihood ratio

“…'s and rank statistics and formulate the corresponding theorem. The proof of this theorem is based on our lemma and [1][2][3][26][27][28][29]. A complete proof will be presented in [9].…”

“…under alternatives play an important role in the asymptotic theory of testing hypotheses (see, e.g., [2, 4, 6-7, 10, 11, 13-15]). Many authors [1,2,7,24] used a.e. for the investigation of asymptotic efficiency [15] and deficiencies of tests [1,2,28].…”

“…Many authors [1,2,7,24] used a.e. for the investigation of asymptotic efficiency [15] and deficiencies of tests [1,2,28]. Besides improving the accuracy of numerical calculations, these expansions may be used for obtaining a.e.…”

Asymptotic normality of generalized L-statistics with unbounded scores

“…Let us take X=IR, m=2 and where we have used the formula displayed at the top of page 128 of Albers et al (1976) to compute the double integral in (4.7). It follows from (4.4), (4.6) and (4.7) that (4.8)…”