Search results for " Normal"

showing 10 items of 336 documents

Holt–Winters Forecasting: An Alternative Formulation Applied to UK Air Passenger Data

2007

Abstract This paper provides a formulation for the additive Holt–Winters forecasting procedure that simplifies both obtaining maximum likelihood estimates of all unknowns, smoothing parameters and initial conditions, and the computation of point forecasts and reliable predictive intervals. The stochastic component of the model is introduced by means of additive, uncorrelated, homoscedastic and Normal errors, and then the joint distribution of the data vector, a multivariate Normal distribution, is obtained. In the case where a data transformation was used to improve the fit of the model, cumulative forecasts are obtained here using a Monte-Carlo approximation. This paper describes the metho…

Statistics and ProbabilityExponential smoothingData transformation (statistics)Prediction intervalMultivariate normal distributionJoint probability distributionHomoscedasticityStatisticsEconometricsStatistics Probability and UncertaintyTime seriesPhysics::Atmospheric and Oceanic PhysicsSmoothingMathematicsJournal of Applied Statistics
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The conditional censored graphical lasso estimator

2020

© 2020, Springer Science+Business Media, LLC, part of Springer Nature. In many applied fields, such as genomics, different types of data are collected on the same system, and it is not uncommon that some of these datasets are subject to censoring as a result of the measurement technologies used, such as data generated by polymerase chain reactions and flow cytometer. When the overall objective is that of network inference, at possibly different levels of a system, information coming from different sources and/or different steps of the analysis can be integrated into one model with the use of conditional graphical models. In this paper, we develop a doubly penalized inferential procedure for…

Statistics and ProbabilityFOS: Computer and information sciencesComputer scienceGaussianInferenceData typeTheoretical Computer Sciencehigh-dimensional settingDatabase normalizationMethodology (stat.ME)symbols.namesakeLasso (statistics)Graphical modelConditional Gaussian graphical modelcensored graphical lassoStatistics - MethodologyHigh-dimensional settingconditional Gaussian graphical modelssparsityEstimatorCensoring (statistics)Censored graphical lassoComputational Theory and MathematicssymbolsCensored dataStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaSparsityAlgorithm
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Local Asymptotic Normality for Shape and Periodicity in the Drift of a Time Inhomogeneous Diffusion

2017

We consider a one-dimensional diffusion whose drift contains a deterministic periodic signal with unknown periodicity $T$ and carrying some unknown $d$-dimensional shape parameter $\theta$. We prove Local Asymptotic Normality (LAN) jointly in $\theta$ and $T$ for the statistical experiment arising from continuous observation of this diffusion. The local scale turns out to be $n^{-1/2}$ for the shape parameter and $n^{-3/2}$ for the periodicity which generalizes known results about LAN when either $\theta$ or $T$ is assumed to be known.

Statistics and ProbabilityLocal asymptotic normalityMathematical analysisLocal scale62F12 60J60020206 networking & telecommunicationsMathematics - Statistics Theory02 engineering and technologyStatistics Theory (math.ST)01 natural sciencesShape parameterPeriodic function010104 statistics & probability0202 electrical engineering electronic engineering information engineeringFOS: Mathematics0101 mathematicsDiffusion (business)Mathematics
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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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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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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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