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Natural Gradient Flow in the Mixture Geometry of a Discrete Exponential Family [PDF]
Entropy, 2015 In this paper, we study Amari’s natural gradient flows of real functions defined on the densities belonging to an exponential family on a finite sample space.
Luigi Malagò, Giovanni Pistone
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On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families [PDF]
Mathematics, 2021 Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:Θ→Θ,θ⟼gn(θ ...
Shaul K. Bar-Lev
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Increasing Hazard Rate of Mixtures for Natural Exponential Families [PDF]
Advances in Applied Probability, 2012 Hazard rates play an important role in various areas, e.g. reliability theory, survival analysis, biostatistics, queueing theory, and actuarial studies. Mixtures of distributions are also of great preeminence in such areas as most populations of components are indeed heterogeneous.
Shaul K. Bar‐Lev, Gérard Letac
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Bayesian approach to cubic natural exponential families [PDF]
Statistics & Probability Letters, 2013 For a natural exponential family (NEF), one can associate in a natural way two standard families of conjugate priors, one on the natural parameter and the other on the mean parameter. These families of conjugate priors have been used to establish some remarkable properties and characterization results of the quadratic NEF's.
Marwa Hamza, Abdelhamid Hassairi
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A Natural Identity for Exponential Families with Applications in Multiparameter Estimation [PDF]
The Annals of Statistics, 1978 A random variable $X$ is said to have distribution in the class $\mathscr{E}_0$ if, for some real valued, positive function $a(\bullet)$, the identity $E\{(X - \mu)g(X)\} = E\{a(X)g'(X)\}$ holds for any absolutely continuous real valued function $g(\bullet)$ satisfying $E|a(X)g'(X)| 2$.
Harold Hudson
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Nonparametric regression in natural exponential families [PDF]
, 2010 Theory and methodology for nonparametric regression have been particularly well developed in the case of additive homoscedastic Gaussian noise. Inspired by asymptotic equivalence theory, there have been ongoing efforts in recent years to construct explicit procedures that turn other function estimation problems into a standard nonparametric regression ...
Tianxi Cai, Harrison H. Zhou
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Reproducibility and Natural Exponential Families with Power Variance Functions [PDF]
The Annals of Statistics, 1986 Let $X_1, \cdots, X_n$ be i.i.d. r.v.'s having common distribution belonging to a family $\mathscr{F} = \{F_\theta: \theta \in \Theta \subset R\}$ indexed by a parameter $\theta$. $\mathscr{F}$ is said to be reproducible if there exists a sequence $\{\alpha(n)\}$ such that $\mathscr{L}(\alpha(n)\sum^n_{i=1} X_i) \in \mathscr{F}$ for all $\theta \in ...
Shaul K. Bar‐Lev, Peter Enis
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Natural Exponential Families with Quadratic Variance Functions: Statistical Theory [PDF]
The Annals of Statistics, 1983 The normal, Poisson, gamma, binomial, negative binomial, and NEFGHS distributions are the six univariate natural exponential families (NEF) with quadratic variance functions (QVF). This sequel to Morris (1982) treats certain statistical topics that can be handled within this unified NEF-QVF formulation, including unbiased estimation, Bhattacharyya and ...
Carl N. Morris
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Laplace Approximations for Natural Exponential Families with Cuts [PDF]
Scandinavian Journal of Statistics, 1998 Standard and fully exponential form Laplace approximations to marginal densities are described and conditions under which these give exact answers are investigated. A general result is obtained and is subsequently applied in the case of natural exponential families with cuts, in order to derive the marginal posterior density of the mean parameter ...
M. Efstathiou +2 more
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Small area estimation with spatially varying natural exponential families [PDF]
Journal of Statistical Computation and Simulation, 2020 Two-stage hierarchical models have been widely used in small area estimation to produce indirect estimates of areal means. When the areas are treated exchangeably and the model parameters are assumed to be the same over all areas, we might lose the efficiency in the presence of spatial heterogeneity.
Shonosuke Sugasawa +2 more
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