Crossing balanced and stair nested desings

Balanced nesting is the most usual form of nesting and originates, when used singly or with crossing of such sub-models, orthogonal models. In balanced nesting we are forced to divide repeatedly the plots and we have few degrees of freedom for the first levels. If we apply stair nesting we will have plots all of the same size rendering the designs easier to apply. The stair nested designs are a valid alternative for the balanced nested designs because we can work with fewer observations, the amount of information for the different factors is more evenly distributed and we obtain good results. The inference for models with balanced nesting is already well studied. For models with stair nesting it is easy to carry out inference because it is very similar to that for balanced nesting. Furthermore stair nested designs being unbalanced have an orthogonal structure. Other alternative to the balanced nesting is the staggered nesting that is the most popular unbalanced nested design which also has the advantage of requiring fewer observations. However staggered nested designs are not orthogonal, unlike the stair nested designs. In this work we start with the algebraic structure of the balanced, the stair and the staggered nested designs and we finish with the structure of the cross between balanced and stair nested designs

Analysis of residuals and adjustment in JRA

Joint Regression Analysis (JRA) is based in linear regression applied to yields, adjusting one linear regression per cultivar. The environmental indexes in JRA correspond to a non observable regressor which measures the productivity of the blocks in the field trials. Usually zig-zag algorithm is used in the adjustment. In this algorithm, minimizations for the regression coefficients alternate with those for the environmental indexes. The algorithm has performed very nicely but a general proof of convergence to the absolute minimum of the sum of squares of residues is still lucking. We now present a model for the residues that may be used to validate the adjustments carried out by the zig-zag algorithm

Subsídios para uma teoria estatística do problema da classificação

info:eu-repo/semantics/publishedVersio

Joint regression analysis applied to genotype stability evaluation over years

Most genotype differences connected with yield stability are due to genotype environment interaction. The presence and dimension of this interaction are the factors that determine the performance of genotypes in distinct environments. The environmental factors, like annual rainfall, temperature, diseases or soil fertility, can only explain part of this interaction. Many statistical tools have been developed with the aim to explain the information contained in the GE interaction data matrix. In our work we use the Joint Regression Analysis (JRA), the Zig-Zag Algorithm to estimate the regression coefficients and the multiple comparison tests of Scheffé, Tukey and Bonferroni. We point out not just the limitations of the JRA when used year by year, but also genotype selection advantage from general JRA over years. Data of the Portuguese Plant Breeding Board were used to carry the year and over years analyses of yielding stability of 22 different genotypes of oat (Avena sativa L.) at six different locations in the years 2002, 2003 and 2004.info:eu-repo/semantics/publishedVersio

Multi-treatment regression analysis: the unbalanced case

Under multi-treatment regression analysis, instead of a sample for each treatment of a linear model, there is a linear regression in the same variables. Then, instead of the action of the treatments on the sample mean values, the action on regression coefficients is studied. When data is unbalanced, the regression matrices differs between regressions. This problem is solved through the use of a block-wise diagonal covariance matrix in the ANOVA procedures. The methodology was then applied to data obtained from experiments of electrodialtic removal of 3 heavy metals from contaminated wood. First, polynomial regressions of the 4th and 3rd were fitted to each metal concentration in the electrolytes through time. Then the unbalanced case of multi-treatment regression analysis was applied aiming to choose the best treatment in jointly removing the 3 metals. Results pointed to the choice of treatment 1 as the most efficient.authorsversionpublishe

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 observations than the usual cross balanced nested designs and it is easy to carry out inference

Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications

Selected papers of the 17th Congress of the Portuguese Statistical Society, covering recent advances in Statistics, particularly in Regression, Extreme values, Markov processes and statistical applications in several areas

Inference for L orthogonal models

A mixed model Yo = ∑m i=1 Xiβi + ∑i=m+1 w Xiβ̃ + e is orthogonal when the matrices Mi = XiXi T, i = 1,...,w, commute. The vectors βc1 1,...,βcm m are fixed vectors and the βcm+1 m+1,...,βcw w and en are random. For these models we have very interesting results namely we have UMVUE for the relevant parameters when normality is assumed. We now intend to generalize that class of models taking Y = L(∑i=1 mXiβi + ∑i=m+1 w Xiβ̃ + e with L a matrix whose column vectors are linearly independent.authorsversionpublishe

On a sufficient condition for commutative orthogonal block structure

A model has orthogonal block structure if it has variancecovariance matrix that is a linear combination of known pairwise orthogonal orthogonal projection matrices that add to the identity matrix. When the orthogonal projection matrix on the space spanned by the mean vector commutes with the orthogonal projection matrices, in the expression of the variance-covariance matrix, the model has commutative orthogonal block structure. Resorting to B-matrices we present a general condition for this commutativity

Extracting Portuguese-Spanish word translations from aligned parallel texts

This paper describes a method for extracting Portuguese–Spanish word translation equivalents from aligned parallel texts. This method uses the standard loglikelihood statistics to measure the similarity between two words. Parallel texts are aligned using a simple method that extends previous work by Pascale Fung & Kathleen McKeown and Melamed. In contrast, the method in this paper does not use statistically unsupported heuristics to filter reliable correspondence points. Instead, it provides the statistical support those authors could not claim by using confidence bands of linear regressions. The points of the linear regression line are generated from the positions of homograph words which occur with the same frequency in parallel text segments. With this alignment method, we are able to extract word translation equivalents (about 90 of the best 100 are correct equivalents).This research was partially supported by a grant from Fundação para a Ciência e Tecnologia / Praxis XXI