Binary operations on commutative Jordan algebras are used to carry out the ANOVA of a two layer model. The treatments in the first layer nests those in the second layer, that being a sub-model for each treatment in the first layer. We present an application with data retried from agricultural experiments.
En el modelo de regresión lineal y = E(Y/X = x) = θx, donde (X,Y) es un vector aleatorio bidimensional, del que se dispone de una muestra {(X1, Y1), ..., (Xn, Yn)}, se han introducido recientemente una clase general de estimadores para θ definida como aquellos valores que minimizan el funcional:ψ(θ) = ∫ (αn(x) - θx)2 dΩn(x)donde αn es un estimador no paramétrico del tipo núcleo o histograma para α(x) = E(Y/X = x) y Ωn una función de ponderación.En este trabajo se extiende tal estudio cuando inicialmente...
Given a base design with quantitative factors and a primary linear regression to each of the treatments, we may adjust secondary regressions of linear combinations of the adjusted coefficients on the primary regressions on the factor levels, thus obtaining a biregressional model. A biregressional design was established for a set of treatments, defined from quantitative factors and a linear regression in the same variables. Afterwards the action of the regression coefficients...
Many data sets analyzed in human and social sciences have a multilevel or hierarchical structure. By hierarchy we mean that units of a certain level (also referred micro units) are grouped into, or nested within, higher level (or macro) units. In these cases, the units within a cluster tend to be more different than units from other clusters, i.e., they are correlated. Thus, unlike in the classical setting where there exists a single source of variation between observational units, the heterogeneity...
Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to...
For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw and Croux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared with that of...
We consider a multivariate regression (growth curve) model of the form , , , where and ’s are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters estimating simultaneously the first and the second order parameters.
By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant in the MGM model , , scalar , with a matrix . A known random matrix has the expected value , where the matrix is a known matrix of an experimental design, is an unknown matrix of parameters and is the covariance matrix of being the symbol of the Kronecker...