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Algebraic structure for the crossing of balanced and stair nested designs

Célia Fernandes, Paulo Ramos, João Tiago Mexia (2014)

Discussiones Mathematicae Probability and Statistics

Stair nesting allows us to work with fewer observations than the most usual form of nesting, the balanced nesting. In the case of stair nesting the amount of information for the different factors is more evenly distributed. This new design leads to greater economy, because we can work with fewer observations. In this work we present the algebraic structure of the cross of balanced nested and stair nested designs, using binary operations on commutative Jordan algebras. This new cross requires fewer...

Algebraic structureof step nesting designs

Célia Fernandes, Paulo Ramos, João Tiago Mexia (2010)

Discussiones Mathematicae Probability and Statistics

Step nesting designs may be very useful since they require fewer observations than the usual balanced nesting models. The number of treatments in balanced nesting design is the product of the number of levels in each factor. This number may be too large. As an alternative, in step nesting designs the number of treatments is the sum of the factor levels. Thus these models lead to a great economy and it is easy to carry out inference. To study the algebraic structure of step nesting designs we introduce...

Algunas soluciones aproximadas para diseños split-plot con matrices de covarianza arbitrarias.

Guillermo Vallejo Seco, José Ramón Escudero García (1998)

Qüestiió

El presente trabajo revisa con cierto detalle diversos tipos de análisis para diseños split-plot que carecen del mismo número de unidades experimentales dentro de cada grupo y en los que se incumple el supuesto de esfericidad multimuestral. Específicamente, adoptando el enfoque multivariado de aproximar los grados de libertad desarrollado por Johansen (1980) y el procedimiento de aproximación general mejorada corregida basado en Huynh (1980) se muestra cómo obtener análisis robustos y poderosos...

Aligned rank tests in measurement error model

Radim Navrátil, A. K. Md. Ehsanes Saleh (2016)

Applications of Mathematics

Aligned rank tests are introduced in the linear regression model with possible measurement errors. Unknown nuisance parameters are estimated first and then classical rank tests are applied on the residuals. Two situations are discussed: testing about an intercept in the linear regression model considering the slope parameter as nuisance and testing of parallelism of several regression lines, i.e. whether the slope parameters of all lines are equal. Theoretical results are derived and the simulation...

All about the ⊥ with its applications in the linear statistical models

Augustyn Markiewicz, Simo Puntanen (2015)

Open Mathematics

For an n x m real matrix A the matrix A⊥ is defined as a matrix spanning the orthocomplement of the column space of A, when the orthogonality is defined with respect to the standard inner product ⟨x, y⟩ = x'y. In this paper we collect together various properties of the ⊥ operation and its applications in linear statistical models. Results covering the more general inner products are also considered. We also provide a rather extensive list of references

An adaptive method of estimation and outlier detection in regression applicable for small to moderate sample sizes

Brenton R. Clarke (2000)

Discussiones Mathematicae Probability and Statistics

In small to moderate sample sizes it is important to make use of all the data when there are no outliers, for reasons of efficiency. It is equally important to guard against the possibility that there may be single or multiple outliers which can have disastrous effects on normal theory least squares estimation and inference. The purpose of this paper is to describe and illustrate the use of an adaptive regression estimation algorithm which can be used to highlight outliers, either single or multiple...

An alternative analysis of variance.

Nicholas T. Longford (2008)

SORT

The one-way analysis of variance is a staple of elementary statistics courses. The hypothesis test of homogeneity of the means encourages the use of the selected-model based estimators which are usually assessed without any regard for the uncertainty about the outcome of the test. We expose the weaknesses of such estimators when the uncertainty is taken into account, as it should be, and propose synthetic estimators as an alternative.

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