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Misclassified multinomial data: a Bayesian approach.

Carlos Javier Pérez, F. Javier Girón, Jacinto Martín, Manuel Ruiz, Carlos Rojano (2007)

RACSAM

In this paper, the problem of inference with misclassified multinomial data is addressed. Over the last years there has been a significant upsurge of interest in the development of Bayesian methods to make inferences with misclassified data. The wide range of applications for several sampling schemes and the importance of including initial information make Bayesian analysis an essential tool to be used in this context. A review of the existing literature followed by a methodological discussion is...

Misclassified size-biased modified power series distribution and its applications

Anwar Hassan, Peer Bilal Ahmad (2009)

Mathematica Bohemica

A misclassified size-biased modified power series distribution (MSBMPSD) where some of the observations corresponding to x = 2 are misclassified as x = 1 with probability α , is defined. We obtain its recurrence relations among ordinary, central and factorial moments and also for some of its particular cases like the size-biased generalized negative binomial (SBGNB) and the size-biased generalized Poisson (SBGP) distributions. We also discuss the effect of the misclassification on the variance for MSBMPSD...

Model selection with vague prior information

Elias Moreno, F. Javier Girón, M. Lina Martínez (1998)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

In the Bayesian approach, the Bayes factor is the main tool for model selection and hypothesis testing. When prior information is weak, "default" or "automatic" priors, which are typicaIly improper, are commonly used but, unfortunately, the Bayes factor is defined up to a multiplicative constant. In this paper we revise some recent but already popular methodologies, intrinsic and lractional, to deal with improper priors in model selection and hypothesis testing. Special attention is paid to the...

Modeling biased information seeking with second order probability distributions

Gernot D. Kleiter (2015)

Kybernetika

Updating probabilities by information from only one hypothesis and thereby ignoring alternative hypotheses, is not only biased but leads to progressively imprecise conclusions. In psychology this phenomenon was studied in experiments with the “pseudodiagnosticity task”. In probability logic the phenomenon that additional premises increase the imprecision of a conclusion is known as “degradation”. The present contribution investigates degradation in the context of second order probability distributions....

Modelización de datos longitudinales con estructuras de covarianza no estacionarias: modelos de coeficientes aleatorios frente a modelos alternativos.

Vicente Núñez-Antón, Dale L. Zimmerman (2001)

Qüestiió

Un tema que ha suscitado el interés de los investigadores en datos longitudinales durante las dos últimas décadas, ha sido el desarrollo y uso de modelos paramétricos explícitos para la estructura de covarianza de los datos. Sin embargo, el análisis de estructuras de covarianza no estacionarias en el contexto de datos longitudinales no se ha realizado de forma detallada principalmente debido a que las distintas aplicaciones no hacían necesario su uso. Muchos son los modelos propuestos recientemente,...

Moderate deviations for two sample t-statistics

Hongyuan Cao (2007)

ESAIM: Probability and Statistics

Let X1,...,Xn1 be a random sample from a population with mean µ1 and variance σ 1 2 , and X1,...,Xn1 be a random sample from another population with mean µ2 and variance σ 2 2 independent of {Xi,1 ≤ i ≤ n1}. Consider the two sample t-statistic T = X ¯ - Y ¯ - ( μ 1 - μ 2 ) s 1 2 / n 1 + s 2 2 / n 2 . This paper shows that ln P(T ≥ x) ~ -x²/2 for any x := x(n1,n2) satisfying x → ∞, x = o(n1 + n2)1/2 as n1,n2 → ∞ provided 0 < c1 ≤ n1/n2 ≤ c2 < ∞. If, in addition, E|X1|3 < ∞, E|Y1|3 < ∞, then P ( T x ) 1 - Φ ( x ) 1 holds uniformly in x ∈ (O,o((n1 + n2)1/6))

Modified minimax quadratic estimation of variance components

Viktor Witkovský (1998)

Kybernetika

The paper deals with modified minimax quadratic estimation of variance and covariance components under full ellipsoidal restrictions. Based on the, so called, linear approach to estimation variance components, i. e. considering useful local transformation of the original model, we can directly adopt the results from the linear theory. Under normality assumption we can can derive the explicit form of the estimator which is formally find to be the Kuks–Olman type estimator.

Modified power divergence estimators in normal models – simulation and comparative study

Iva Frýdlová, Igor Vajda, Václav Kůs (2012)

Kybernetika

Point estimators based on minimization of information-theoretic divergences between empirical and hypothetical distribution induce a problem when working with continuous families which are measure-theoretically orthogonal with the family of empirical distributions. In this case, the φ -divergence is always equal to its upper bound, and the minimum φ -divergence estimates are trivial. Broniatowski and Vajda [3] proposed several modifications of the minimum divergence rule to provide a solution to the...

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