Statistical inference on the shape of multivariate curves: mode detection, level set estimation and classification

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The purpose of the project is to develop flexible nonparametric procedures for making inference on the shape of multivariate curves. For multivariate curves several new problems arise, which are not present in the more well studied one dimensional case. We propose research to be done on mode detection, level set estimation and classification. Number and location of modes give a first impression on the shape of a curve. Estimation of modes is typically based on searches of regions where observations are concentrated. This is connected to the estimation of level sets of densities. On the other hand, when designing classification procedures one has to find optimal decision sets. Techniques to find optimal decision sets are often closely related to techniques for the estimation of level sets. The research proposal includes work to be done both in mathematical analysis of statistical procedures and also designing of fast algorithms and graphical tools. We intend to implement algorithms and distribute software in addition to the publication of the results.