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Scaling of model approximation errors and expected entropy distances

Guido F. Montúfar, Johannes Rauh (2014)

Kybernetika

We compute the expected value of the Kullback-Leibler divergence of various fundamental statistical models with respect to Dirichlet priors. For the uniform prior, the expected divergence of any model containing the uniform distribution is bounded by a constant $1 - γ$ . For the models that we consider this bound is approached as the cardinality of the sample space tends to infinity, if the model dimension remains relatively small. For Dirichlet priors with reasonable concentration parameters the expected...

Second order asymptotic distribution of the $R_{φ}$ -divergence goodness-of-fit statistics

María Del Carmen Pardo (2000)

Kybernetika

The distribution of each member of the family of statistics based on the $R_{φ}$ -divergence for testing goodness-of-fit is a chi-squared to $o (1)$ (Pardo [pard96]). In this paper a closer approximation to the exact distribution is obtained by extracting the $φ$ -dependent second order component from the $o (1)$ term.

Sequential estimation in processes with independent increments

Wolfgang Winkler (1980)

Banach Center Publications

Sequential statistical structures

H. Heckendorff (1980)

Banach Center Publications

Seules les affinités préservent le type de la loi gamma à paramètre entier

C. Hassenforder (1990)

Annales de l'I.H.P. Probabilités et statistiques

Several applications of divergence criteria in continuous families

Michel Broniatowski, Igor Vajda (2012)

Kybernetika

This paper deals with four types of point estimators based on minimization of information-theoretic divergences between hypothetical and empirical distributions. These were introduced (i) by Liese and Vajda [9] and independently Broniatowski and Keziou [3], called here power superdivergence estimators, (ii) by Broniatowski and Keziou [4], called here power subdivergence estimators, (iii) by Basu et al. [2], called here power pseudodistance estimators, and (iv) by Vajda [18] called here Rényi pseudodistance...

Sobre el tamaño de muestra para experimentos aleatorios con imprecisión difusa.

M.ª Angeles Gil Alvarez, Pedro Gil Alvarez (1988)

Trabajos de Estadística

Statistical Inference deals with the drawing of conclusions about a random experiment on the basis of the information contained in a sample from it. A random experiment can be defined by means of the set of its possible outcomes (sample space) and the ability of observation of the experimenter. It is usually assumed that this ability allows the experimenter to describe the observable events as subsets of the sample space. In this paper, we will consider that the experimenter can only express the...

Solution of a Statistical Optimization Problem by Rearrangement Methods.

L. Rüschendorf (1983)

Metrika

Some counterexamples concerning sufficiency and invariance.

R. H. Berk, A. G. Nogales, J. A. Oyola (1995)

Extracta Mathematicae

Some inequalities related to the Stam inequality

Abram Kagan, Tinghui Yu (2008)

Applications of Mathematics

Zamir showed in 1998 that the Stam classical inequality for the Fisher information (about a location parameter) $1 / I (X + Y) \geq 1 / I (X) + 1 / I (Y)$ for independent random variables $X$ , $Y$ is a simple corollary of basic properties of the Fisher information (monotonicity, additivity and a reparametrization formula). The idea of his proof works for a special case of a general (not necessarily location) parameter. Stam type inequalities are obtained for the Fisher information in a multivariate observation depending on a univariate location...

Some investigations in minimax estimation theory [Book]

Stanisław Trybuła (1985)

Some measures of the amount of information for the linear regression model.

Mihoc, Ion, Fătu, Cristina–Ioana (2008)

Acta Universitatis Apulensis. Mathematics - Informatics

Some remarks on sufficiency, invariance and conditional independence.

A. G. Nogales, J. A. Oyola (1995)

Extracta Mathematicae

Some results concerning maximum Rényi entropy distributions

Oliver Johnson, Christophe Vignat (2007)

Annales de l'I.H.P. Probabilités et statistiques

Some results envolving the concepts of moment generating function and affinity between distribution functions. Extension for r k-dimensional normal distribution functions.

Antonio Dorival Campos (1999)

Qüestiió

We present a function ρ (F1, F2, t) which contains Matusita's affinity and expresses the affinity between moment generating functions. An interesting results is expressed through decomposition of this affinity ρ (F1, F2, t) when the functions considered are k-dimensional normal distributions. The same decomposition remains true for other families of distribution functions. Generalizations of these results are also presented.

Some results for the quadratic analysis of Gaussian processes and applications

J. Soler (1980)

Banach Center Publications

Some results on a doubly truncated generalized discrimination measure

Suchandan Kayal, Rajesh Moharana (2016)

Applications of Mathematics

Doubly truncated data appear in some applications with survival and astrological data. Analogous to the doubly truncated discrimination measure defined by Misagh and Yari (2012), a generalized discrimination measure between two doubly truncated non-negative random variables is proposed. Several bounds are obtained. It is remarked that the proposed measure can never be equal to a nonzero constant which is independent of the left and right truncated points. The effect of monotone transformations on...

Some results on exponential families of Markov processes

Uwe Küchler (1985)

Banach Center Publications

Some statistical inferences regarding population diversity in terms of the hypoentropy measure.

Domingo Morales, Inder Jeet Taneja, Leandro Pardo (1991)

Trabajos de Estadística

We consider a measure of the diversity of a population based on the λ-measure of hypoentropy introduced by Ferreri (1980). Our purpose is to study its asymptotic distribution for testing hypotheses. A numerical example based on real data is given.

Stability of invariant linearly sufficient statistics in the general Gauss-Markov model

Andrzej Kornacki (1997)

Applications of Mathematics

Necessary and sufficient conditions are derived for the inclusions $J_{0} \subset J$ and $J_{0}^{*} \subset J^{*}$ to be fulfilled where $J_{0}$ , $J_{0}^{*}$ and $J$ , $J^{*}$ are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models $G M_{0} = (y, X_{0} β_{0}, σ_{0}^{2} V_{0})$ and $G M = (y, X β, σ^{2} V)$ , respectively.

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