Calibrating the excess mass and dip tests of modality

M.-Y. Cheng, Peter Hall

Research output: Contribution to journalJournal articlepeer-review

66 Citations (Scopus)


Nonparametric tests of modality are a distribution-free way of assessing evidence about inhomogeneity in a population, provided that the potential sub populations are sufficiently well separated. They include the excess mass and dip tests, which are equivalent in univariate settings and are alternatives to the bandwidth test. Only very conservative forms of the excess mass and dip tests are available at presently, however, and for that reason they are generally not competitive with the bandwidth test. In the present paper we develop a practical approach to calibrating the excess mass and dip tests to improve their level accuracy and power substantially. Our method exploits the fact that the limiting distribution of the excess mass statistic under the null hypothesis depends on unknowns only through a constant, which may be estimated. Our calibrated test exploits this fact and is shown to have greater power and level accuracy than the bandwidth test has. The latter tends to be quite conservative, even in an asymptotic sense. Moreover, the calibrated test avoids difficulties that the bandwidth test has with spurious modes in the tails, which often must be discounted through subjective intervention of the experimenter.
Original languageEnglish
Pages (from-to)579-589
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number3
Publication statusPublished - Dec 1998


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