A Further Note on the Asymptotic Efficiency of Friedman's xr2-Test.
A Geometric Appraoch to Finite Sample and Large Deviation Properties in Two-Way ANOVA with Spherically Distributed Error Vectors.
A Gram-Schmidt orthogonalizing process of design matrices in linear models as an estimating procedure of covariance components.
Se considera un modelo lineal mixto multivariante equilibrado sin interacción para el que las matrices de las formas cuadráticas necesarias para estimar la covarianza de las componentes se expresan mediante operadores lineales en espacios con producto interior de dimensión finita. El propósito de este artículo es demostrar que las formas cuadráticas obtenidas por el proceso de ortogonalización de Gram-Schmidt de las matrices de diseño son combinaciones lineales de las formas cuadráticas derivadas...
A minimax property of translation invariant estimators for variance components
A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models
We consider a construction of approximate confidence intervals on the variance component in mixed linear models with two variance components with non-zero degrees of freedom for error. An approximate interval that seems to perform well in such a case, except that it is rather conservative for large was considered by Hartung and Knapp in [hk]. The expression for its asymptotic coverage when suggests a modification of this interval that preserves some nice properties of the original and that...
A simplified treatment of the restricted analysis of a slightly disproportionate factorial experiment.
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...
A statistical variance components framework for mapping imprinted quantitative trait locus in experimental crosses.
About the best linear unbiased predictor (BLUP) and associated restrictions. (Sobre la construcción del mejor predictor lineal insesgado (BLUP) y restricciones asociadas.)
Admissibility of Henderson's estimators for three variance components
Admissible invariant estimators in a linear model
Let be observation vector in the usual linear model with expectation and covariance matrix known up to a multiplicative scalar, possibly singular. A linear statistic is called invariant estimator for a parametric function if its MSE depends on only through . It is shown that is admissible invariant for , if and only if, it is a BLUE of in the case when is estimable with zero variance, and it is of the form , where and is an arbitrary BLUE, otherwise. This result is used in...
Affine resolvable incomplete block designs
Ajustement linéaire lorsque les deux variables sont soumises à des erreurs de variances hétérogènes
Algebraic structure for the crossing of balanced and stair nested designs
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
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...
Algorithm 38. Calculation of all marginal means from an n-way table
Algorithm 39. Evaluation of corrected sums of squares for analysis of variance in a factorial design with n factors
Algorithm 40. Search for marginal means at given factor levels in an n-way table containing data scores and all marginal means
Algunas soluciones aproximadas para diseños split-plot con matrices de covarianza arbitrarias.
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...
An alternative analysis of variance.
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.
An application of analysis of covariance to response surface