1,720,983 research outputs found
Nonparametric Mode Hunting
No full textWe 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
SuRF: Subspace Ridge Finder
No full textThis paper deals with a nonparametric method for estimating the ridges of a density function. Ridge estimation is useful for understanding the structure of a density. It can also be used to find hidden structure in point cloud data: when the data are noisy measurements of a manifold, under mild conditions the ridges are close and topologically similar to the hidden manifold. We propose a new estimation procedure called SuRF and study its rate of convergence
Consistenza degli stimatori di massima verosimiglianza e della probabilita' a posteriori: un approccio unificante - Quaderno di Dipartimento Serie A - Ricerche n.2-2000 - Dipartimento di Statistica, Probabilità e Statistiche Applicate - Università degli Studi di Roma "La Sapienza"
No full textSerie A - Ricerche n.2, (2000
Non-parametric inference for density modes
No full textWe derive non-parametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a data-splitting approach in which potential modes are identified by using the first half of the data and inference is done with the second half of the data. To obtain valid confidence sets for the eigenvalues, we use a bootstrap based on an elementary symmetric polynomial transformation. This leads to valid bootstrap confidence sets regardless of any multiplicities in the eigenvalues. We also suggest a new method for bandwidth selection, namely choosing the bandwidth to maximize the number of significant modes. We show by example that this method works well. Even when the true distribution is singular, and hence does not have a density (in which case cross-validation chooses a zero bandwidth), our method chooses a reasonable bandwidth
- …
