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Unimodality and Exponential Families
Communications in Statistics - Simulation and Computation, 1973Relationships between uninodality, strong unimodality and canonical exponential families axe studied. Furthermore, some considerations axe given pertaining to the duality viewpoint as applied to the sampling and the likelihood aspects of statistical models.
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Cuts in Natural Exponential Families
Theory of Probability & Its Applications, 1996The concept of cuts [\textit{O. E. Barndorff-Nielsen}, Exponential families and conditioning. Sc. D. Thesis, Univ. Copenhagen (1973; Zbl 0297.62001)], which is intimately connected to the concepts of \(S\)-ancillarity and \(S\)-sufficiency, has been studied in the context of general exponential families.
Barndorff-Nielsen, O. E., Koudou, A. E.
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Stability for Multivariate Exponential Families
Journal of Mathematical Sciences, 2001Let \(E\) be a Euclidean space, let \(Z :\Omega\to E\) be a nondegenerate random vector, and suppose there is an open convex set \(D\subset E\) such that \(P(Z\in \overline{D}) = 1\). If \(\mu\) is the distribution of \(Z\), define measures \(\mu_\lambda\) by \(d\mu_\lambda(x) = e^{\lambda x}d\mu(x)\), \(x\in E\), for any \(\lambda\) in the dual space \
Balkema, A. A. +2 more
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2009
Curved exponential families may arise when the parameters of an exponential family satisfy constraints. For these families the minimal sufficient statistic may not be complete, and UMVU estimation may not be possible. Curved exponential families arise naturally with data from sequential experiments, considered in Section 5.2, and Section 5.3 considers ...
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Curved exponential families may arise when the parameters of an exponential family satisfy constraints. For these families the minimal sufficient statistic may not be complete, and UMVU estimation may not be possible. Curved exponential families arise naturally with data from sequential experiments, considered in Section 5.2, and Section 5.3 considers ...
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Nonlinear exponential families
1993The nonlinear regression model $$\begin{array}{*{20}{c}} {y = \eta \left( \vartheta \right) + \varepsilon ;\quad \left( {\vartheta \in \Theta } \right),} \\ {\varepsilon \sim N\left( {0,{{\sigma }^{2}}W} \right)} \\ \end{array}$$ considered in previous chapters, can be presented equivalently as a family of densities $$\left\{ {f(y\left ...
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Information Property of Exponential Families
Theory of Probability & Its Applications, 1986See the review in Zbl 0582.60022.
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Exponential Families and Game Dynamics
Canadian Journal of Mathematics, 1982A symmetric game consists of a set of pure strategies indexed by {0, …, n} and a real payoff matrix (aij). When two players choose strategies i and j the payoffs are aij and aji to the i-player and j-player respectively. In classical game theory of Von Neumann and Morgenstern [16] the payoffs are measured in units of utility, i.e., desirability, or in
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2012
Exponential families of distributions are parametric dominated families in which the logarithm of probability densities take a simple bilinear form (bilinear in the parameter and a statistic). As a consequence of that special form, sampling models in those families admit a finite-dimensional sufficient statistic irrespective of the sample size, and ...
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Exponential families of distributions are parametric dominated families in which the logarithm of probability densities take a simple bilinear form (bilinear in the parameter and a statistic). As a consequence of that special form, sampling models in those families admit a finite-dimensional sufficient statistic irrespective of the sample size, and ...
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