 On mode testing and empirical approximations to distributionsMing-Yen Cheng and Peter Hall Statistics & Probability Letters, 1998, vol. 39, issue 3, 245-254 Abstract: There are close connections between the theory of statistical inference under order restrictions and the theory of tests for unimodality. In particular, a result of Kiefer and Wolfowitz, on the error of convex approximations to empirical distribution functions, is basic to limit theory for the dip test for unimodality. We develop a version of Kiefer and Wolfowitz' result in the context of distributions that are strongly unimodal, and apply it and related limit theory to compare the powers, against local alternatives, of three different tests of unimodality. In this context it is shown that the dip, excess mass and bandwidth tests are all able to detect departures of size n-3/5 (measured in terms of the distribution function) from the null hypothesis, where n denotes sample size; but are not able to detect departures of smaller order. Thus, they have similar powers. Keywords: Bandwidth; test; Concave; majorant; Convex; minorant; Density; estimation; Dip; test; Excess; mass; test; Local; alternative; hypothesis; Order; constraints; Unimodal; distribution (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:39:y:1998:i:3:p:245-254 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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