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A simplified treatment of the restricted analysis of a slightly disproportionate factorial experiment.

José M. Prieto, José M. Caridad (1988)

Qüestiió

This paper considers a procedure to obtain effect estimators in the least squares analysis of a slightly disproportionate factorial design when a sample survey is made of the results of an extensive experiment. Explicit formulae have been found for the restricted estimators and their variances, when the constraints normally imposed upon a proportional model are used. In addition, an approximate analysis of the original model is used to perform that estimation, and an approximate analysis of variance...

Análisis de diseños factoriales sin replicación.

Jesús Juan, Daniel Peña (1991)

Trabajos de Estadística

En este artículo se propone un método para identificar efectos significativos en diseños factoriales sin replicación, resolviendo el problema como un caso de determinación de observaciones atípicas (outliers) en muestras altamente contaminadas. Para ello se deriva un estimador robusto de escala basándose en simulaciones realizadas con ordenador. El método es extremadamente sencillo de aplicar y conduce a los mismos resultados que el proyectado por Box y Meyer (1986) que es de mayor complejidad.

Control treatments in designs with split units generated by Latin squares

Shinji Kuriki, Iwona Mejza, Kazuhiro Ozawa, Stanisław Mejza (2014)

Biometrical Letters

This paper deals with two-factor experiments with split units. The whole plot treatments occur in a repeated Latin square, modified Latin square or Youden square, while subplot treatments occur in a block design within the whole plots. The statistical properties of the considered designs are examined. Special attention is paid to the case where one of the treatments is an individual control or an individual standard treatment. In addition, we give a brief overview of work on the design of experiments...

Cross additivity - an application

Sandra Saraiva Ferreira, Dário Ferreira, João Tiago Mexia (2006)

Discussiones Mathematicae Probability and Statistics

We try to show that Discriminant Analysis can be considered as a branch of Statistical Decision Theory when viewed from a Bayesian approach. First we present the necessary measure theory results, next we briefly outline the foundations of Bayesian Inference before developing Discriminant Analysis as an application of Bayesian Estimation. Our approach renders Discriminant Analysis more flexible since it gives the possibility of classing an element as belonging to a group of populations. This possibility...

Estudio de la producción de energía eléctrica de una dinamo movida por una turbina hidráulica mediante diseños factoriales.

M. Albea Rodríguez, E. Villar Mesa (1991)

Qüestiió

Este artículo es el resultado de una práctica voluntaria de carácter académico, referida al temario de la asignatura de Estadística de tercer curso de la Escuela de Ingenieros Industriales.Por tanto, el objetivo principal es ver cómo mediante un conjunto reducido de experimentos, el diseño fraccional permite extraer información de un proceso o sistema sometido a la influencia de un número elevado de factores.

Factorial experimental designs and generalized linear models.

Simplice Dossou-Gbété, Walter Tinsson (2005)

SORT

This paper deals with experimental designs adapted to a generalized linear model. We introduce a special link function for which the orthogonality of design matrix obtained under Gaussian assumption is preserved. We investigate by simulation some of its properties.

Inference for random effects in prime basis factorials using commutative Jordan algebras

Vera M. Jesus, Paulo Canas Rodrigues, João Tiago Mexia (2007)

Discussiones Mathematicae Probability and Statistics

Commutative Jordan algebras are used to drive an highly tractable framework for balanced factorial designs with a prime number p of levels for their factors. Both fixed effects and random effects models are treated. Sufficient complete statistics are obtained and used to derive UMVUE for the relevant parameters. Confidence regions are obtained and it is shown how to use duality for hypothesis testing.

Inverting covariance matrices

Czesław Stępniak (2006)

Discussiones Mathematicae Probability and Statistics

Some useful tools in modelling linear experiments with general multi-way classification of the random effects and some convenient forms of the covariance matrix and its inverse are presented. Moreover, the Sherman-Morrison-Woodbury formula is applied for inverting the covariance matrix in such experiments.

Note on the ANOVA of a completely confounded factorial experiment

Wiktor Oktaba (2005)

Applicationes Mathematicae

The purpose of this paper is to present a modern approach to the analysis of variance (ANOVA) of disconnected resolvable group divisible partially balanced incomplete block (GDPBIB) designs with factorial structure and with some interaction effects completely confounded. A characterization of a factorial experiment with completely confounded interaction is given. The treatment effect estimators and some relations between the matrix F of the reduced normal equations and the information matrix A are...

Optimal chemical balance weighing designs for v + 1 objects

Bronisław Ceranka, Małgorzata Graczyk (2003)

Kybernetika

The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for p = v objects implies the existence of an optimum chemical balance weighing design for p = v + 1 objects are given. The existence of an optimum chemical balance weighing design for p = v + 1 objects implies the existence of an optimum chemical...

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