We propose a procedure for detecting the modes of a density estimate and test their significance. We use a data-splitting approach: potential modes are identified using the first half of the data and their significance is tested with the second half of the data. The mode test is based on nonparametric confidence intervals for the eigenvalues of the Hessian. In order to get valid bootstrap confidence sets even in presence of multiplicity of the eigenvalues, we use a bootstrap based on an elementary-symmetric-polynomial transformation.

Nonparametric Mode Hunting / Perone Pacifico, Marco. - 47th SIS Scientific Meeting of the Italian Statistical Society, (2014), pp. - (47th Scientific Meeting of the Italian Statistical Society

Nonparametric Mode Hunting

Marco Perone Pacifico
2014

Abstract

We propose a procedure for detecting the modes of a density estimate and test their significance. We use a data-splitting approach: potential modes are identified using the first half of the data and their significance is tested with the second half of the data. The mode test is based on nonparametric confidence intervals for the eigenvalues of the Hessian. In order to get valid bootstrap confidence sets even in presence of multiplicity of the eigenvalues, we use a bootstrap based on an elementary-symmetric-polynomial transformation.
978-88-8467-874-4
bootstrap; density estimation; elementary symmetric polynomials; modes
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/182615
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