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Making use of incomplete observations for regression in bivariate normal model

Joanna Tarasińska (2003)

Applications of Mathematics

Two estimates of the regression coefficient in bivariate normal distribution are considered: the usual one based on a sample and a new one making use of additional observations of one of the variables. They are compared with respect to variance. The same is done for two regression lines. The conclusion is that the additional observations are worth using only when the sample is very small.

Marginal problem, statistical estimation, and Möbius formula

Martin Janžura (2007)

Kybernetika

A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood...

Markov bases of conditional independence models for permutations

Villő Csiszár (2009)

Kybernetika

The L-decomposable and the bi-decomposable models are two families of distributions on the set S n of all permutations of the first n positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these Markov bases, we show that not all bi-decomposable distributions can be approximated arbitrarily well by...

Markov operators and n-copulas

P. Mikusiński, M. D. Taylor (2009)

Annales Polonici Mathematici

We extend the definition of Markov operator in the sense of J. R. Brown and of earlier work of the authors to a setting appropriate to the study of n-copulas. Basic properties of this extension are studied.

Matrix rank and inertia formulas in the analysis of general linear models

Yongge Tian (2017)

Open Mathematics

Matrix mathematics provides a powerful tool set for addressing statistical problems, in particular, the theory of matrix ranks and inertias has been developed as effective methodology of simplifying various complicated matrix expressions, and establishing equalities and inequalities occurred in statistical analysis. This paper describes how to establish exact formulas for calculating ranks and inertias of covariances of predictors and estimators of parameter spaces in general linear models (GLMs),...

Measuring association via lack of co-monotonicity: the LOC index and a problem of educational assessment

Danang Teguh Qoyyimi, Ricardas Zitikis (2015)

Dependence Modeling

Measuring association, or the lack of it, between variables plays an important role in a variety of research areas, including education,which is of our primary interest in this paper. Given, for example, student marks on several study subjects, we may for a number of reasons be interested in measuring the lack of comonotonicity (LOC) between the marks, which rarely follow monotone, let alone linear, patterns. For this purpose, in this paperwe explore a novel approach based on a LOCindex,which is...

Medida de asociación propia entre variables aleatorias discretas.

María del Carmen Carollo Limeres (1984)

Trabajos de Estadística e Investigación Operativa

En este trabajo estudiamos la asociación entre dos variables aleatorias discretas (no cardinales) definiendo una nueva medida [de] asociación, la cual está basada en la velocidad de convergencia del vector de probabilidad correspondiente a la cadena de Markov asociada a la distribución de probabilidad conjunta de las variables en estudio. Ponemos especial énfasis en el estudio muestral y propiedades de los estimadores de dicha medida, calculando sus distribuciones asintóticas bajo el muestreo multinomial...

Medidas de asociación y dependencia bi-variante.

Concepción Fernández Vivas (1983)

Trabajos de Estadística e Investigación Operativa

El interrogante que vertebra este trabajo puede formularse así:¿Bajo qué condiciones es invertible la implicación X(ω), Y(ω) independientes ⇒ cov (X, Y) = 0 para v.a. no normales?La literatura estadística de los últimos años contiene en forma dispersa modelos interesantes de interdependencia de v.a. que adecuadamente combinados con la incorrelación pueden conducir a la independencia en situaciones de no-gaussianidad. Nuestra intención aquí es agruparlos sistemáticamente, ofreciéndolos en una línea...

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