Search results for "DEPENDENCE"

showing 10 items of 2462 documents

k-Step shape estimators based on spatial signs and ranks

2010

In this paper, the shape matrix estimators based on spatial sign and rank vectors are considered. The estimators considered here are slight modifications of the estimators introduced in Dümbgen (1998) and Oja and Randles (2004) and further studied for example in Sirkiä et al. (2009). The shape estimators are computed using pairwise differences of the observed data, therefore there is no need to estimate the location center of the data. When the estimator is based on signs, the use of differences also implies that the estimators have the so called independence property if the estimator, that is used as an initial estimator, has it. The influence functions and limiting distributions of the es…

Statistics and ProbabilityInfluence functionCovariance matrixApplied MathematicsAffiinisti ekvivarianttitehokkuusspatiaalinen järjestyslukuEstimatorSpatial signEfficiencyM-estimatorEfficient estimatorinfluenssifunktioExtremum estimatorHeavy-tailed distributionStatisticsAffine equivarianceStatistics Probability and UncertaintySpatial rankInvariant estimatorIndependence (probability theory)Mathematicsspatiaalinen merkki
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Pairwise Markov properties for regression graphs

2016

With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of conditional distributions, named regressions in joint responses. The involved random variables may be discrete, continuous or of both types. Such a generating process specifies for each response a conditioning set that contains just its regressor variables, and it leads to at least one valid ordering of all nodes in the corresponding regression graph that has three types of edge: one for undirected dependences among context variables, another for undirect…

Statistics and ProbabilityMarkov chain010102 general mathematicsMixed graphConditional probability distribution01 natural sciencesCombinatorics010104 statistics & probabilityConditional independenceJoint probability distributionMarkov property0101 mathematicsStatistics Probability and UncertaintyMarginal distributionRandom variableMathematicsStat
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Bayesian Mapping of Lichens Growing on Trees

2001

Suitability of trees as hosts for epiphytic lichens are studied in a forest stand of size 25 ha. Suitability is measured as occupation probabilites which are modelled using hierarchical Bayesian approach. These probabilities are useful for an ecologist. They give smoothed spatial distribution map of suitability for each of the species and can be used in detecting high- and low-probability areas. In addition, suitability is explained by tree-level covariates. Spatial dependence, which is due to unobserved spatially structured covariates, is modelled through an unobserved Markov random field. Markov chain Monte Carlo method has been applied in Bayesian computation. The extensive spatial data …

Statistics and ProbabilityMarkov chainbiologyBayesian probabilityDiameter at breast heightMarkov chain Monte CarloGeneral Medicinebiology.organism_classificationsymbols.namesakeStatisticsCovariatesymbolsStatistics Probability and UncertaintySpatial dependenceSpatial analysisMathematicsLobaria pulmonariaBiometrical Journal
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Gaussian component mixtures and CAR models in Bayesian disease mapping

2012

Hierarchical Bayesian models involving conditional autoregression (CAR) components are commonly used in disease mapping. An alternative model to the proper or improper CAR is the Gaussian component mixture (GCM) model. A review of CAR and GCM models is provided in univariate settings where only one disease is considered, and also in multivariate situations where in addition to the spatial dependence between regions, the dependence among multiple diseases is analyzed. A performance comparison between models using a set of simulated data to help illustrate their respective properties is reported. The results show that both in univariate and multivariate settings, both models perform in a comp…

Statistics and ProbabilityMultivariate statisticsApplied MathematicsGaussianBayesian probabilityUnivariateVariable-order Bayesian networkComputational Mathematicssymbols.namesakeComputational Theory and MathematicsAutoregressive modelStatisticsRange (statistics)symbolsEconometricsSpatial dependenceMathematicsComputational Statistics & Data Analysis
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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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On (n-l)-wise and joint independence and normality of n Random variables: an example

1981

An example is given of a vector of n random variables such that any (n-1)-dimensional subvector consists of n-1 independent standard normal variables. The whole vector however is neither independent nor normal.

Statistics and ProbabilityPairwise independenceCombinatoricsExchangeable random variablesIndependent and identically distributed random variablesStandard normal deviateMultivariate random variableSum of normally distributed random variablesStatisticsMarginal distributionCentral limit theoremMathematicsCommunications in Statistics - Theory and Methods
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Quantum correlations in generalized spin star system

2006

The problem of detecting quantum signatures in the correlations formed in dynamical evolution of quantum bipartite systems receives a lot of attention in current literature. Generally speaking, the occurrence of correlations between two observables of a system does not necessarily reflect nonclassical behaviour. In this paper, the exact dynamics of a pair of uncoupled spins 1/2 interacting with a common spin 1/2 bath is investigated. Starting from a separable initial condition, the ability of the system to develop purely quantum correlations is brought to light. Physical interpretation of the concurrence function as well as a suggestion on how to measure it are given.

Statistics and ProbabilityPhysicsDISSOCIATION-CONSTANTSQuantum discordQuantum dynamicsTETRAETHYLAMMONIUM IODIDEStatistical and Nonlinear PhysicsObservable25 DEGREES CSODIUM-CHLORIDEHEAT-CAPACITIESIONIC-STRENGTH DEPENDENCEMOLECULAR-WEIGHTQuantum mechanicsQuantum processQuantum operationQuantum algorithmACTIVITY-COEFFICIENTSIONIZATION-CONSTANTQuantumCOMPLEX-FORMATIONMathematical PhysicsSpin-½
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Selecting the tuning parameter in penalized Gaussian graphical models

2019

Penalized inference of Gaussian graphical models is a way to assess the conditional independence structure in multivariate problems. In this setting, the conditional independence structure, corresponding to a graph, is related to the choice of the tuning parameter, which determines the model complexity or degrees of freedom. There has been little research on the degrees of freedom for penalized Gaussian graphical models. In this paper, we propose an estimator of the degrees of freedom in $$\ell _1$$ -penalized Gaussian graphical models. Specifically, we derive an estimator inspired by the generalized information criterion and propose to use this estimator as the bias term for two informatio…

Statistics and ProbabilityStatistics::TheoryKullback–Leibler divergenceKullback-Leibler divergenceComputer scienceGaussianInformation Criteria010103 numerical & computational mathematicsModel complexityModel selection01 natural sciencesTheoretical Computer Science010104 statistics & probabilitysymbols.namesakeStatistics::Machine LearningGeneralized information criterionEntropy (information theory)Statistics::MethodologyGraphical model0101 mathematicsPenalized Likelihood Kullback-Leibler Divergence Model Complexity Model Selection Generalized Information Criterion.Model selectionEstimatorStatistics::ComputationComputational Theory and MathematicsConditional independencesymbolsPenalized likelihoodStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaAlgorithmStatistics and Computing
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Spatial Mark-Recapture Method in the Estimation of Crayfish Population Size

1995

The mark-recapture method is considered for estimation of population size of slowly moving animals like crayfish. The Petersen type estimator for closed population is generalized for situations where recaptures are spatially dependent between the capture sites, and its variance approximation is derived using point processes as models for the population. The method of quadratic forms is suggested to be used as variance estimator. Finally, a trapping design is proposed where onc trap at recapture is replaced by four adjacent traps. A simulation experiment is performed to explain the robusticity of the new trapping design against movements of animals.

Statistics and Probabilityeducation.field_of_studyPopulation sizePopulationEstimatorGeneral MedicineTrappingCrayfishPoint processMark and recaptureStatisticsStatistics Probability and UncertaintySpatial dependenceeducationMathematicsBiometrical Journal
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Residuenanalyse des Unabhängigkeitsmodells Zweier Kategorialer Variablen

1985

For the ‘cellwise’ analysis of independence of two categorial variables, Haberman (1973) proposes the method of ‘adjusted residuals’. Fuchs and Kenett (1980) use (the absolute value of) the maximal adjusted residual as a measure for the deviation from the null hypothesis.

StatisticsIndependence (mathematical logic)Absolute value (algebra)ResidualNull hypothesisMeasure (mathematics)Categorical variableMathematics
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