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 32. Construction of polynomial values orthogonal on given set of one-dimensional variable
Algorithm 33. Test for difference in trends in a two-factor experiment with repeated measurements
Algorithm 34. Use of orthogonal components in tests for trend
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
Algorithm 44. An abbreviated method of calculating the Mahalanobis distance or residual sum of squares in a linear regression model
Algorithm 55. Multiple regression with stepwise selection of variables
Algorithm 84. The choice of representative variables by stepwise regression
Algorithms. 49. PIECE LIN REGR. An algorithm for fitting discontinuous multiphase linear least-square regression
Algorithms for Optimal Design with Application to Multiple Polynomial Regression.
Algoritmy. 46. COR. Lineární regresní polynom s vedlejší podmínkou
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...
Aligned rank tests in measurement error model
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
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
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 algorithm for reduction of complexity of relations in a system of variables
Let us have a system of variables, among which there are complicated dependences. Assuming reflexivity and transitivity of the relation " depends on ", a simple algorithm is proposed which produces all dependences in an optimized way, without losing information.