Feature significance for multivariate kernel density estimation

Publisher:
Elsevier
Publication Type:
Journal Article
Citation:
Computational Statistics and Data Analysis, 2008, 52 (9), pp. 4225 - 4242
Issue Date:
2008-01
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Multivariate kernel density estimation provides information about structure in data. Feature significance is a technique for deciding whether featuressuch as local extremaare statistically significant. This paper proposes a framework for feature significance in d-dimensional data which combines kernel density derivative estimators and hypothesis tests for modal regions. For the gradient and curvature estimators distributional properties are given, and pointwise test statistics are derived. The hypothesis tests extend the two-dimensional feature significance ideas of Godtliebsen et al. [Godtliebsen, F., Marron, J.S., Chaudhuri, P., 2002. Significance in scale space for bivariate density estimation. Journal of Computational and Graphical Statistics 11, 121]. The theoretical framework is complemented by novel visualization for three-dimensional data. Applications to real data sets show that tests based on the kernel curvature estimators perform well in identifying modal regions. These results can be enhanced by corresponding tests with kernel gradient estimators.
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