Location-adaptive density estimation and nearest-neighbor distance
Journal of Multivariate Analysis
Clustering Algorithms
Bump hunting in high-dimensional data
Statistics and Computing
Journal of Multivariate Analysis
Estimation of regression contour clusters---an application of the excess mass approach to regression
Journal of Multivariate Analysis
Nonparametric density estimation and clustering in astronomical sky surveys
Computational Statistics & Data Analysis
Journal of Multivariate Analysis
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Multivariate mode hunting is of increasing practical importance. Only a few such methods exist, however, and there usually is a trade-off between practical feasibility and theoretical justification. In this paper we attempt to do both. We propose a method for locating isolated modes (or better, modal regions) in a multivariate data set without pre-specifying their total number. Information on significance of the findings is provided by means of formal testing for the presence of antimodes. Critical values of the tests are derived from large sample considerations. The method is designed to be computationally feasible in moderate dimensions, and it is complemented by diagnostic plots. Since the null hypothesis under consideration is highly composite the proposed tests involve calibration in order to ensure a correct (asymptotic) level. Our methods are illustrated by application to real data sets.