Search results for " 62L20"

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Fast Estimation of the Median Covariation Matrix with Application to Online Robust Principal Components Analysis

2017

International audience; The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at each new observation and are able to deal rapidly with large samples of high dimensional data without being obliged to store all the data in memory. Asymptotic convergence properties of the recursive algorithms are studied under weak conditions. The computation of the principal components can also be performed online and this approach can be useful for online outlier detection. A simulation study clearly shows that this robust indicat…

Statistics and ProbabilityComputer scienceMathematics - Statistics TheoryStatistics Theory (math.ST)01 natural sciences010104 statistics & probabilityMatrix (mathematics)Dimension (vector space)Geometric medianStochastic gradientFOS: Mathematics0101 mathematicsL1-median010102 general mathematicsEstimator[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]Geometric medianCovariance[ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH]Functional dataMSC: 62G05 62L20Principal component analysisProjection pursuitAnomaly detectionRecursive robust estimationStatistics Probability and UncertaintyAlgorithm
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Synchronization and fluctuations for interacting stochastic systems with individual and collective reinforcement

2020

The Pólya urn is the paradigmatic example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose a.s. time-limit is not random anymore. In this work, in the stream of previous recent works, we introduce a new family of (finite) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one componentwise, one collective) are tuned through (possibly) different rates n −γ. In the case the reinforcement rates are like n −1 , these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead …

[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Interacting random systemssynchronisation[MATH] Mathematics [math]Almost sure convergenceReinforced stochastic processes[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]62P35Secondary 62L2060F05Central limit theoremsFluctuationsFluctuations MSC2010 Classification Primary 60K3560F15[MATH]Mathematics [math]stable convergence
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