Search results for "uncertainty"

showing 10 items of 1010 documents

Efficient Simulation of Multivariate Binomial and Poisson Distributions

1998

Power investigations, for example, in statistical procedures for the assessment of agreement among multiple raters often require the simultaneous simulation of several dependent binomial or Poisson distributions to appropriately model the stochastical dependencies between the raters' results. Regarding the rather large dimensions of the random vectors to be generated and the even larger number of interactions to be introduced into the simulation scenarios to determine all necessary information on their distributions' dependence stucture, one needs efficient and fast algorithms for the simulation of multivariate Poisson and binomial distributions. Therefore two equivalent models for the mult…

Statistics and ProbabilityPoisson binomial distributionNegative binomial distributionContinuity correctionGeneral MedicinePoisson distributionBinomial distributionsymbols.namesakeUnivariate distributionCompound Poisson distributionStatisticssymbolsApplied mathematicsStatistics Probability and UncertaintyMathematicsCount dataBiometrical Journal
researchProduct

Functional Principal Component Analysis for the explorative analysis of multisite-multivariate air pollution time series with long gaps

2013

The knowledge of the urban air quality represents the first step to face air pollution issues. For the last decades many cities can rely on a network of monitoring stations recording concentration values for the main pollutants. This paper focuses on functional principal component analysis (FPCA) to investigate multiple pollutant datasets measured over time at multiple sites within a given urban area. Our purpose is to extend what has been proposed in the literature to data that are multisite and multivariate at the same time. The approach results to be effective to highlight some relevant statistical features of the time series, giving the opportunity to identify significant pollutants and…

Statistics and ProbabilityPollutantFunctional principal component analysisgeographyMultivariate statisticsgeography.geographical_feature_categorySeries (mathematics)Computer scienceAir pollutionFunctional data analysiscomputer.software_genreUrban areamedicine.disease_causeAir quality Functional Data Analysis Three mode FPCA EOFmedicineData miningStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaAir quality indexcomputer
researchProduct

Exploring regression structure with graphics

1993

We investigate the extent to which it may be possible to carry out a regression analysis using graphics alone, an idea that we refer to asgraphical regression. The limitations of this idea are explored. It is shown that graphical regression is theoretically possible with essentially no constraints on the conditional distribution of the response given the predictors, but with some conditions on marginal distribution of the predictors. Dimension reduction subspaces and added variable plots play a central role in the development. The possibility of useful methodology is explored through two examples.

Statistics and ProbabilityPolynomial regressionEconometricsSufficient dimension reductionPartial regression plotRegression analysisCross-sectional regressionConditional probability distributionStatistics Probability and UncertaintyMarginal distributionSegmented regressionMathematicsTest
researchProduct

Linear and ellipsoidal restrictions in linear regression

1991

The problem of combining linear and ellipsoidal restrictions in linear regression is investigated. Necessary and sufficient conditions for compactness of the restriction set are proved assuring the existence of a minimax estimator. When the restriction set is not compact a minimax estimator may still exist for special loss functions arid regression designs

Statistics and ProbabilityPolynomial regressionStatistics::TheoryMathematical optimizationProper linear modelLinear predictor functionBayesian multivariate linear regressionLinear regressionLinear modelPrincipal component regressionStatistics Probability and UncertaintySimple linear regressionMathematicsStatistics
researchProduct

Affine equivariant multivariate rank methods

2003

The classical multivariate statistical methods (MANOVA, principal component analysis, multivariate multiple regression, canonical correlation, factor analysis, etc.) assume that the data come from a multivariate normal distribution and the derivations are based on the sample covariance matrix. The conventional sample covariance matrix and consequently the standard multivariate techniques based on it are, however, highly sensitive to outlying observations. In the paper a new, more robust and highly efficient, approach based on an affine equivariant rank covariance matrix is proposed and outlined. Affine equivariant multivariate rank concept is based on the multivariate Oja (Statist. Probab. …

Statistics and ProbabilityPure mathematicsApplied MathematicsMatrix t-distributionMultivariate normal distributionNormal-Wishart distributionCombinatoricsEstimation of covariance matricesScatter matrixStatistics::MethodologyMatrix normal distributionMultivariate t-distributionStatistics Probability and UncertaintyMathematicsMultivariate stable distributionJournal of Statistical Planning and Inference
researchProduct

Produits aléatoires d'opérateurs matrices de transfert

1988

Nous etudions le comportement asymptotique de produits aleatoires d'operateurs de Ruelle-Perron-Frobenius. Nous etendons le travail de Ruelle obtenu dans le cas homogene, au cas aleatoire.

Statistics and ProbabilityPure mathematicsErgodic theoryStatistics Probability and UncertaintyAnalysisMathematicsProbability Theory and Related Fields
researchProduct

On decoupling in Banach spaces

2021

AbstractWe consider decoupling inequalities for random variables taking values in a Banach space X. We restrict the class of distributions that appear as conditional distributions while decoupling and show that each adapted process can be approximated by a Haar-type expansion in which only the pre-specified conditional distributions appear. Moreover, we show that in our framework a progressive enlargement of the underlying filtration does not affect the decoupling properties (in particular, it does not affect the constants involved). As a special case, we deal with one-sided moment inequalities for decoupled dyadic (i.e., Paley–Walsh) martingales and show that Burkholder–Davis–Gundy-type in…

Statistics and ProbabilityPure mathematicsGeneral MathematicsBanach space01 natural sciences010104 statistics & probabilityFOS: MathematicsFiltration (mathematics)decoupling in Banach spaces0101 mathematicsSpecial casestokastiset prosessitMathematicsMathematics::Functional Analysisdyadic martingalesProbability (math.PR)010102 general mathematicsDecoupling (cosmology)Conditional probability distributionBanachin avaruudetAdapted processMoment (mathematics)regular conditional probabilities60E15 60H05 46B09stochastic integrationStatistics Probability and UncertaintyfunktionaalianalyysiRandom variableMathematics - Probability
researchProduct

Some Remarks on Exponential Families

1987

Abstract The following facts may serve to provide a feeling about how restrictive the assumption of an exponential family is. (a) A one-parameter exponential family in standard form with respect to Lebesgue measure is a location parameter family iff it is normal with fixed variance. (b) It is a scale parameter family iff it is gamma with fixed shape parameter. Both facts are known (see Borges and Pfanzagl 1965; Ferguson 1962; Lindley 1958) but may not have received as much attention as they deserve. Under the assumption of differentiable densities, short and elementary proofs are given.

Statistics and ProbabilityPure mathematicsLocation parameterLebesgue measureGeneral MathematicsLocation-scale familyShape parameterExponential familyCalculusDifferentiable functionStatistics Probability and UncertaintyNatural exponential familyScale parameterMathematicsThe American Statistician
researchProduct

Infinite rate mutually catalytic branching in infinitely many colonies: The longtime behavior

2012

Consider the infinite rate mutually catalytic branching process (IMUB) constructed in [Infinite rate mutually catalytic branching in infinitely many colonies. Construction, characterization and convergence (2008) Preprint] and [Ann. Probab. 38 (2010) 479-497]. For finite initial conditions, we show that only one type survives in the long run if the interaction kernel is recurrent. On the other hand, under a slightly stronger condition than transience, we show that both types can coexist.

Statistics and ProbabilityPure mathematicsProbability (math.PR)coexistenceType (model theory)Characterization (mathematics)Branching (polymer chemistry)Trotter productstochastic differential equationsLévy noisesegregation of typesStochastic differential equationKernel (algebra)Mutually catalytic branching60G1760K35Convergence (routing)FOS: Mathematics60J6560J55PreprintStatistics Probability and UncertaintyMathematics - ProbabilityMathematicsBranching processThe Annals of Probability
researchProduct

Remarks on ergodicity and invariant occupation measure in branching diffusions with immigration☆

2005

Abstract We give a necessary and sufficient condition for ergodicity with finite invariant occupation measure for branching diffusions with immigration. We do not assume uniformly subcritial reproduction means. We discuss the structure of the invariant occupation measure and of its density.

Statistics and ProbabilityPure mathematicsProbability theoryErgodicityMathematical analysisQuantitative Biology::Populations and EvolutionInvariant measureStatistics Probability and UncertaintyInvariant (mathematics)Ergodic processResolventMathematicsAnnales de l'Institut Henri Poincare (B) Probability and Statistics
researchProduct