Search results for "Normal"

showing 10 items of 2571 documents

Recursive estimation of the conditional geometric median in Hilbert spaces

2012

International audience; A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirm…

Statistics and ProbabilityMallows-Wasserstein distanceRobbins-Monroasymptotic normalityCLTcentral limit theoremAsymptotic distributionMathematics - Statistics TheoryStatistics Theory (math.ST)01 natural sciencesMallows–Wasserstein distanceonline data010104 statistics & probability[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]60F05FOS: MathematicsApplied mathematics[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]0101 mathematics62L20MathematicsaveragingSequential estimation010102 general mathematicsEstimatorRobbins–MonroConditional probability distribution[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]Geometric medianstochastic gradient[ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH]robust estimatorRate of convergenceConvergence of random variablesStochastic gradient.kernel regressionsequential estimationKernel regressionStatistics Probability and Uncertainty
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Statistics of return times for weighted maps of the interval

2000

For non markovian, piecewise monotonic maps of the interval associated to a potential, we prove that the law of the entrance time in a cylinder, when renormalized by the measure of the cylinder, converges to an exponential law for almost all cylinders. Thanks to this result, we prove that the fluctuations of Rn, first return time in a cylinder, are lognormal.

Statistics and ProbabilityMathematical analysisMarkov processMonotonic functionCylinder (engine)law.inventionPhysics::Fluid DynamicsReturn timesymbols.namesakelawLog-normal distributionPiecewisesymbolsStatistics Probability and UncertaintyExponential lawMathematicsAnnales de l'Institut Henri Poincare (B) Probability and Statistics
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A more efficient second order blind identification method for separation of uncorrelated stationary time series

2016

The classical second order source separation methods use approximate joint diagonalization of autocovariance matrices with several lags to estimate the unmixing matrix. Based on recent asymptotic results, we propose a novel unmixing matrix estimator which selects the best lag set from a finite set of candidate sets specified by the user. The theory is illustrated by a simulation study.

Statistics and ProbabilityMathematical optimizationaffine equivarianceminimum distance indexasymptotic normalityAsymptotic distributionlinear process01 natural sciencesSet (abstract data type)010104 statistics & probabilityMatrix (mathematics)SOBIComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION0502 economics and businessSource separationjoint diagonalization0101 mathematicsFinite set050205 econometrics Mathematicsta112Series (mathematics)05 social sciencesEstimatorAutocovarianceStatistics Probability and UncertaintyAlgorithmStatistics & Probability Letters
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Some links between conditional and coregionalized multivariate Gaussian Markov random fields

2020

Abstract Multivariate disease mapping models are attracting considerable attention. Many modeling proposals have been made in this area, which could be grouped into three large sets: coregionalization, multivariate conditional and univariate conditional models. In this work we establish some links between these three groups of proposals. Specifically, we explore the equivalence between the two conditional approaches and show that an important class of coregionalization models can be seen as a large subclass of the conditional approaches. Additionally, we propose an extension to the current set of coregionalization models with some new unexplored proposals. This extension is able to reproduc…

Statistics and ProbabilityMultivariate statisticsClass (set theory)Random fieldMarkov chainComputer science0208 environmental biotechnologyUnivariateMultivariate normal distribution02 engineering and technologyManagement Monitoring Policy and Law01 natural sciences020801 environmental engineering010104 statistics & probabilityEstadística bayesianaDiscriminative modelMalaltiesEconometrics0101 mathematicsComputers in Earth SciencesEquivalence (measure theory)Spatial Statistics
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Multivariate nonparametric tests of independence

2005

New test statistics are proposed for testing whether two random vectors are independent. Gieser and Randles, as well as Taskinen, Kankainen, and Oja have introduced and discussed multivariate extensions of the quadrant test of Blomqvist. This article serves as a sequel to this work and presents new multivariate extensions of Kendall's tau and Spearman's rho statistics. Two different approaches are discussed. First, interdirection proportions are used to estimate the cosines of angles between centered observation vectors and between differences of observation vectors. Second, covariances between affine-equivariant multivariate signs and ranks are used. The test statistics arising from these …

Statistics and ProbabilityMultivariate statisticsMultivariate analysisNonparametric statisticsAsymptotic distributionMultivariate normal distributionSpearman's rank correlation coefficientQuadrant testriippumattomuusPitman efficiencyKendall's tauStatisticsHigh-dimensional statisticsaffine invarianceStatistics Probability and UncertaintySpearman's rhoRobustnessMathematicsStatistical hypothesis testing
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On easily interpretable multivariate reference regions of rectangular shape

2011

Till now, multivariate reference regions have played only a marginal role in the practice of clinical chemistry and laboratory medicine. The major reason for this fact is that such regions are traditionally determined by means of concentration ellipsoids of multidimensional Gaussian distributions yielding reference limits which do not allow statements about possible outlyingness of measurements taken in specific diagnostic tests from a given patient or subject. As a promising way around this difficulty we propose to construct multivariate reference regions as p-dimensional rectangles or (in the one-sided case) rectangular half-spaces whose edges determine univariate percentile ranges of the…

Statistics and ProbabilityMultivariate statisticsNonparametric statisticsUnivariateMultivariate normal distributionGeneral MedicineStatisticsApplied mathematicsProbability distributionStatistics Probability and UncertaintyMarginal distributionQuantileParametric statisticsMathematicsBiometrical Journal
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Affine-invariant rank tests for multivariate independence in independent component models

2016

We consider the problem of testing for multivariate independence in independent component (IC) models. Under a symmetry assumption, we develop parametric and nonparametric (signed-rank) tests. Unlike in independent component analysis (ICA), we allow for the singular cases involving more than one Gaussian independent component. The proposed rank tests are based on componentwise signed ranks, à la Puri and Sen. Unlike the Puri and Sen tests, however, our tests (i) are affine-invariant and (ii) are, for adequately chosen scores, locally and asymptotically optimal (in the Le Cam sense) at prespecified densities. Asymptotic local powers and asymptotic relative efficiencies with respect to Wilks’…

Statistics and ProbabilityMultivariate statisticssingular information matricesRank (linear algebra)Gaussianuniform local asymptotic02 engineering and technology01 natural sciencesdistribution-free testsCombinatoricstests for multivariate independence010104 statistics & probabilitysymbols.namesakenormaalius0202 electrical engineering electronic engineering information engineeringApplied mathematics0101 mathematicsStatistique mathématiqueIndependence (probability theory)Parametric statisticsMathematicsDistribution-free testsuniform local asymptotic normalityNonparametric statistics020206 networking & telecommunicationsIndependent component analysisrank testsAsymptotically optimal algorithmsymbolsindependent component models62H1562G35Statistics Probability and UncertaintyUniform local asymptotic normality62G10
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Moments for Some Kumaraswamy Generalized Distributions

2014

Explicit expansions for the moments of some Kumaraswamy generalized (Kw-G) distributions (Cordeiro and de Castro, 2011) are derived using special functions. We explore the Kw-normal, Kw-gamma, Kw-beta, Kw-t, and Kw-F distributions. These expressions are given as infinite weighted linear combinations of well-known special functions for which numerical routines are readily available.

Statistics and ProbabilityNormal distributionSpecial functionsMathematical analysisGeneralized gamma distributionGeneralized beta distributionGeneralized integer gamma distributionLinear combinationInverse distributionVariance-gamma distributionMathematicsCommunications in Statistics - Theory and Methods
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Unacceptable implications of the left haar measure in a standard normal theory inference problem

1978

For a very common statistical problem, inference about the mean of a normal random variable, some inadmissible consequences of the left Haar invariant prior measure, which is that recommended as a suitable prior by Jeffreys’ multivariate rule and by the methods of Villegas and Kashyap, are uncovered and investigated.

Statistics and ProbabilityNormal distributionStatisticsPrior probabilityInferenceHaarStatistics Probability and UncertaintyInvariant (mathematics)Standard normal tableMeasure (mathematics)MathematicsHaar measureTrabajos de Estadistica Y de Investigacion Operativa
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Hybrid recommendation methods in complex networks

2015

We propose here two new recommendation methods, based on the appropriate normalization of already existing similarity measures, and on the convex combination of the recommendation scores derived from similarity between users and between objects. We validate the proposed measures on three relevant data sets, and we compare their performance with several recommendation systems recently proposed in the literature. We show that the proposed similarity measures allow to attain an improvement of performances of up to 20\% with respect to existing non-parametric methods, and that the accuracy of a recommendation can vary widely from one specific bipartite network to another, which suggests that a …

Statistics and ProbabilityNormalization (statistics)Social and Information Networks (cs.SI)FOS: Computer and information sciencesPhysics - Physics and SocietyComputer scienceNonparametric statisticsFOS: Physical sciencesComputer Science - Social and Information NetworksCondensed Matter PhysicPhysics and Society (physics.soc-ph)Complex networkRecommender systemcomputer.software_genreComputer Science - Information RetrievalBipartite graphConvex combinationData miningNoisy datacomputerInformation Retrieval (cs.IR)Statistical and Nonlinear Physic
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