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Calibrating the excess mass and dip tests of modality
Author(s) -
Cheng M.Y.,
Hall P.
Publication year - 1998
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00141
Subject(s) - spurious relationship , bandwidth (computing) , statistics , statistic , nonparametric statistics , population , test statistic , univariate , mathematics , statistical hypothesis testing , computer science , telecommunications , multivariate statistics , demography , sociology
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.