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Linear Hypothesis (linear + hypothesis)
Selected AbstractsLikelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilitiesJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2006Francesco Bartolucci Summary., For a class of latent Markov models for discrete variables having a longitudinal structure, we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process. For the maximum likelihood estimation of a latent Markov model under hypotheses of this type, we outline an EM algorithm that is based on well-known recursions in the hidden Markov literature. We also show that, under certain assumptions, the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent Markov model, against a less stringent linear hypothesis on the transition probabilities of the same model, is of type. As a particular case, we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent Markov version, which may be used to test the hypothesis of absence of transition between latent states. The approach is illustrated through a series of simulations and two applications, the first of which is based on educational testing data that have been collected within the National Assessment of Educational Progress 1996, and the second on data, concerning the use of marijuana, which have been collected within the National Youth Survey 1976,1980. [source] Adjusted Exponentially Tilted Likelihood with Applications to Brain MorphologyBIOMETRICS, Issue 3 2009Hongtu Zhu Summary In this article, we develop a nonparametric method, called adjusted exponentially tilted (ET) likelihood, and apply it to the analysis of morphometric measures. The adjusted exponential tilting estimator is shown to have the same first-order asymptotic properties as that of the original ET likelihood. The adjusted ET likelihood ratio statistic is applied to test linear hypotheses of unknown parameters, such as the associations of brain measures (e.g., cortical and subcortical surfaces) with covariates of interest, such as age, gender, and gene. Simulation studies show that the adjusted exponential tilted likelihood ratio statistic performs as well as the,t -test when the imaging data are symmetrically distributed, while it is superior when the imaging data have skewed distribution. We demonstrate the application of our new statistical methods to the detection of statistically significant differences in the morphology of the hippocampus between two schizophrenia groups and healthy subjects. [source] A geomorphological explanation of the unit hydrograph conceptHYDROLOGICAL PROCESSES, Issue 4 2004C. Cudennec Abstract The water path from any point of a basin to the outlet through the self-similar river network was considered. This hydraulic path was split into components within the Strahler ordering scheme. For the entire basin, we assumed the probability density functions of the lengths of these components, reduced by the scaling factor, to be independent and isotropic. As with these assumptions, we propose a statistical physics reasoning (similar to Maxwell's reasoning) that considers a hydraulic length symbolic space, built on the self-similar lengths of the components. Theoretical expressions of the probability density functions of the hydraulic length and of the lengths of all the components were derived. These expressions are gamma laws expressed in terms of simple geomorphological parameters. We validated our theory with experimental observations from two French basins, which are different in terms of size and relief. From the comparisons, we discuss the relevance of the assumptions and show how a gamma law structure underlies the river network organization, but under the influence of a strong hierarchy constraint. These geomorphological results have been translated into travel time probability density functions, through the hydraulic linear hypothesis. This translation provides deterministic explanations of some famous a priori assumptions of the unit hydrograph and the geomorphological unit hydrograph theories, such as the gamma law general shape and the exponential distribution of residence time in Strahler states. Copyright © 2004 John Wiley & Sons, Ltd. [source] Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilitiesJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2006Francesco Bartolucci Summary., For a class of latent Markov models for discrete variables having a longitudinal structure, we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process. For the maximum likelihood estimation of a latent Markov model under hypotheses of this type, we outline an EM algorithm that is based on well-known recursions in the hidden Markov literature. We also show that, under certain assumptions, the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent Markov model, against a less stringent linear hypothesis on the transition probabilities of the same model, is of type. As a particular case, we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent Markov version, which may be used to test the hypothesis of absence of transition between latent states. The approach is illustrated through a series of simulations and two applications, the first of which is based on educational testing data that have been collected within the National Assessment of Educational Progress 1996, and the second on data, concerning the use of marijuana, which have been collected within the National Youth Survey 1976,1980. [source] A convection scheme for data assimilation: Description and initial testsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 606 2005Philippe Lopez Abstract A new simplified parametrization of subgrid-scale convective processes has been developed and tested in the framework of the ECMWF Integrated Forecasting System for the purpose of variational data assimilation, singular vector calculations and adjoint sensitivity experiments. Its formulation is based on the full nonlinear convection scheme used in ECMWF forecasts, but a set of simplifications has been applied to substantially improve its linear behaviour. These include the specification of a single closure assumption based on convective available potential energy, the uncoupling of the equations for the convective mass flux and updraught characteristics and a unified formulation of the entrainment and detrainment rates. Simplified representations of downdraughts and momentum transport are also included in the new scheme. Despite these simplifications, the forecasting ability of the new convective parametrization is shown to remain satisfactory even in seasonal integrations. A detailed study of its Jacobians and the validity of the linear hypothesis is presented. The new scheme is also tested in combination with the new simplified parametrization of large-scale clouds and precipitation recently developed at ECMWF. In contrast with the simplified convective parametrization currently used in ECMWF's operational 4D-Var, its tangent-linear and adjoint versions account for perturbations of all convective quantities including convective mass flux, updraught characteristics and precipitation fluxes. Therefore the new scheme is expected to be beneficial when combined with radiative calculations that are directly affected by condensation and precipitation. Examples are presented of applications of the new moist physics in 1D-Var retrievals using microwave brightness temperature measurements and in adjoint sensitivity experiments. Copyright © 2005 Royal Meteorological Society. [source] | ||||||||||