This article is cited in 11 papers

Short Communications

Second-order and bootstrap approximation to Student's $t$-statistic

M. Bloznelis^a, H. Putter<sup>b

a</sup> The Faculty of Mathematics and Informatics, Vilnius University
^b Leiden University

Abstract: We prove the validity of one-term Edgeworth expansion for Student's $t$-statistic under minimal conditions: the distribution of observations is nonlattice and has finite third moment. As a corollary we obtain the second-order correctness for the bootstrap of Student's t-statistic under these optimal conditions, thus extending classical result of Singh [Ann. Statist., 9 (1981), pp. 1187–1195] to the Studentized mean.

Keywords: Student test, Edgeworth expansion, bootstrap, asymptotic expansion, self-normalized sum.

Received: 13.05.1999

Language: English

DOI: 10.4213/tvp3669

 English version: Theory of Probability and its Applications, 2003, 47:2, 300–307

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