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The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, subRiemannian manifolds, and Lie groups. In parallel, in geometric mechanics, JeanMarie Souriau interpreted the temperature vector of Planck as a spacetime vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties.
uncertainty relation  Wigner–Yanase–Dyson skew information  quantum memory  Born probability rule  quantumclassical relationship  spinors in quantum and classical physics  square integrable  energy quantization  Quantum HamiltonJacobi Formalism  quantum trajectory  generalized uncertainty principle  successive measurements  minimal observable length  Rényi entropy  Tsallis entropy  deep learning  quantum computing  neuromorphic computing  high performance computing  quantum mechanics  Gleason theorem  Kochen–Specker theorem  Born rule  quantum uncertainty  quantum foundations  quantum information  continuous variables  Bohmian dynamics  entanglement indicators  linear entropy  original Bell inequality  perfect correlation/anticorrelation  qudit states  quantum bound  measure of classicality  foundations of quantum mechanics  uncertainty relations  bell inequalities  entropy  quantum computing
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This book presents new and original research in Statistical Information Theory, based on minimum divergence estimators and test statistics, from a theoretical and applied point of view, for different statistical problems with special emphasis on efficiency and robustness. Divergence statistics, based on maximum likelihood estimators, as well as Wald’s statistics, likelihood ratio statistics and Rao’s score statistics, share several optimum asymptotic properties, but are highly nonrobust in cases of model misspecification under the presence of outlying observations. It is wellknown that a small deviation from the underlying assumptions on the model can have drastic effect on the performance of these classical tests. Specifically, this book presents a robust version of the classical Wald statistical test, for testing simple and composite null hypotheses for general parametric models, based on minimum divergence estimators.
sparse  robust  divergence  MM algorithm  Bregman divergence  generalized linear model  localpolynomial regression  model check  nonparametric test  quasilikelihood  semiparametric model  Wald statistic  composite likelihood  maximum composite likelihood estimator  Wald test statistic  composite minimum density power divergence estimator  Waldtype test statistics  Bregman divergence  general linear model  hypothesis testing  influence function  robust  Waldtype test  loglinear models  ordinal classification variables  association models  correlation models  minimum penalized ?divergence estimator  consistency  asymptotic normality  goodnessoffit  bootstrap distribution estimator  thematic quality assessment  relative entropy  logarithmic super divergence  robustness  minimum divergence inference  generalized renyi entropy  minimum divergence methods  robustness  single index model  model assessment  statistical distance  nonquadratic distance  total variation  mixture index of fit  KullbackLeibler distance  divergence measure  ?divergence  relative error estimation  robust estimation  information geometry  centroid  Bregman information  Hölder divergence  indoor localization  robustness  efficiency  Bayesian nonparametric  Bayesian semiparametric  asymptotic property  minimum disparity methods  Hellinger distance  Berstein von Mises theorem  measurement errors  robust testing  twosample test  misspecified hypothesis and alternative  2alternating capacities  composite hypotheses  corrupted data  leastfavorable hypotheses  Neyman Pearson test  divergence based testing  Chernoff Stein lemma  compressed data  Hellinger distance  representation formula  iterated limits  influence function  consistency  asymptotic normality  locationscale family  n/a
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