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Asymptotic distributions of non-central studentized statistics

Authors Shao, Qiman View this author's profile
Zhang, RongMao
Issue Date 2009
Source Science in China Series a-mathematics , v. 52, (6), 2009, JUN, p. 1262-1284
Summary Let X (1), ..., X (n) be independent and identically distributed random variables and W (n) = W (n) (X (1), ..., X (n) ) be an estimator of parameter I. Denote T (n) = (W (n) - I (0))/s (n) , where s (n) (2) is a variance estimator of W (n) . In this paper a general result on the limiting distributions of the non-central studentized statistic T (n) is given. Especially, when s (n) (2) is the jacknife estimate of variance, it is shown that the limit could be normal, a weighted chi (2) distribution, a stable distribution, or a mixture of normal and stable distribution. Applications to the power of the studentized U- and L- tests are also discussed.
ISSN 1006-9283
Language English
Format Article
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