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作者：Shiers, N.; Zwiernik, P.; Aston, J. A. D.; Smith, J. Q.
作者单位：University of Warwick; Pompeu Fabra University; University of Cambridge; University of Warwick
摘要：We provide a complete description of possible distributions consistent with any Gaussian latent tree model. This description consists of polynomial equations and inequalities involving covariances between the observed variables. Testing inequality constraints can be done using the inverse Wishart distribution and this leads to simple preliminary assessment of tree-compatibility. To test equality constraints we employ general techniques of tetrad analyses. This approach is effective even for sm...
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作者：Alexandrovich, G.; Holzmann, H.; Leister, A.
作者单位：Philipps University Marburg
摘要：Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability matrices have full-rank and are ergodic, and if the state-dependent distributions are all distinct, but not necessarily linearly independent. Based on this identification result, we develop a nonparametric maximum likelihood estimation theory. First, we show that t...
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作者：Broda, Simon A.; Kan, Raymond
作者单位：University of Amsterdam; University of Toronto
摘要：Inversion formulae are derived that express the density and distribution function of a ratio of random variables in terms of the joint characteristic function of the numerator and denominator. The resulting expressions are amenable to numerical evaluation and lead to simple asymptotic expansions. The expansions reduce to known results when the denominator is almost surely positive. Their accuracy is demonstrated with numerical examples.
