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Semiparametrically Efficient Inference based on Signed Ranks in Symmetric Independent Component Models”, (2011)

by P Ilmonen, D Paindaveine
Venue:Annals of Statistics,
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R-estimation for asymmetric independent component analysis

by Marc Hallin, Chintan Mehta - Journal of the American Statistical Association , 2014
"... Independent Component Analysis (ICA) recently has attracted much attention in the statistical literature as an appealing alternative to elliptical models. Whereas k-dimensional elliptical densities depend on one single unspecified radial density, however, k-dimensional independent component distribu ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
Independent Component Analysis (ICA) recently has attracted much attention in the statistical literature as an appealing alternative to elliptical models. Whereas k-dimensional elliptical densities depend on one single unspecified radial density, however, k-dimensional independent component distributions involve k unspecified component densities. In practice, for given sample size n and dimension k, this makes the statistical analysis much harder. We focus here on the estimation, from an independent sample, of the mixing/demixing matrix of the model. Traditional methods (FOBI, Kernel-ICA, FastICA) mainly originate from the engineering literature. Their consistency requires moment conditions, they are poorly robust, and do not achieve any type of asymptotic efficiency. When based on robust scatter matrices, the two-scatter methods developed by Oja et al. (2006) and Nordhausen et al. (2008) enjoy better robustness features, but their optimality properties remain unclear. The “classical semiparametric ” approach by Chen and Bickel (2006), quite on the contrary, achieves semiparametric efficiency, but requires the estimation of the densities of the k unobserved independent compo-

On asymptotics of ICA estimators and their performance indices

by Pauliina Ilmonen, Klaus Nordhausen, Hannu Oja, Esa Ollila , 2012
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A high-dimensional nonparametric multivariate test for mean vector

by Lan Wang , Bo Peng , Runze Li - J. Amer. Statist. Assoc , 2015
"... Abstract This work is concerned with testing the population mean vector of nonnormal high-dimensional multivariate data. Several tests for high-dimensional mean vector have been proposed in the literature, but they may not perform well for high-dimensional continuous, nonnormal multivariate data, w ..."
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Abstract This work is concerned with testing the population mean vector of nonnormal high-dimensional multivariate data. Several tests for high-dimensional mean vector have been proposed in the literature, but they may not perform well for high-dimensional continuous, nonnormal multivariate data, which frequently arise in genomics studies and quantitative finance. This paper aims to develop a novel high-dimensional nonparametric test for the population mean vector so that multivariate normality assumption becomes unnecessary. With the aid of new tools in modern probability theory, we proved that the limiting null distribution of the proposed test is normal under mild conditions for p > n. We further study the local power of the proposed test and compare its relative efficiency with a modified Hotelling T 2 test for high-dimensional data. Our theoretical results indicate that the newly proposed test can have even more substantial power gain than the traditional nonparametric multivariate test does with finite fixed p. We assess the finite sample performance of the proposed test by examining its size and power via Monte Carlo studies. We illustrate the application of the proposed test by an empirical analysis of a genomics data set.

4 Fourth Moments and Independent Component Analysis

by J. Miettinen, S. Taskinen, K. Nordhausen, H. Oja
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by Jari Miettinen, Katrin Illner, Klaus Nordhausen, Hannu Oja, Sara Taskinen, Fabian J. Theis , 2014
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4 QUANTIFYING IDENTIFIABILITY IN INDEPENDENT COMPONENT ANALYSIS

by Alexander Sokol, Marloes H. Maathuis, Benjamin Falkeborg
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... is a semiparametric model, where A is the parameter of interest and R is a nuisance parameter. Asymptotic distributions of estimates of the mixing matrix in this type of set-up are derived in, e.g., =-=[1, 4, 14]-=-. The difficulty of identifying A can then be appraised by considering for example the asymptotic variance of the estimates. Alternatively, one can consider estimation of A for a given error distribut...

Independent Component Analysis

by Marc Hallin, Marc Hallin, Chintan Mehta , 2013
"... Independent Component Analysis (ICA) recently has attracted much attention in the statistical literature as an attractive and useful alternative to elliptical models. Whereas k-dimensional elliptical densities depend on one single unspecified radial density, however, k-dimensional independent compon ..."
Abstract - Add to MetaCart
Independent Component Analysis (ICA) recently has attracted much attention in the statistical literature as an attractive and useful alternative to elliptical models. Whereas k-dimensional elliptical densities depend on one single unspecified radial density, however, k-dimensional independent component distributions involve k unspecified component densities. In practice, for a given sample size n and given dimension k, this makes the statistical analysis much harder. We focus here on the estimation, from an independent sample, of the mixing/demixing matrix of the model. Traditional methods (FOBI, Kernel-ICA, FastICA) mainly originate from the engineering literature. The statistical properties of those methods are not well known, and they typically require very large samples. So does the “classical semiparametric ” approach by Chen and Bickel (2006), which is based on an estimation of the k component densities (those densities being those of the unobserved independent components). The “double scatter matrix ” method of Oja et al. (2006) and (2008) requires the arbitrary choice of two scatter matrices generally based on estimated higher-order moments which are likely
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