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On the equality of the ordinary least squares estimators and the best linear unbiased estimators in multivariate growth-curve models.

Gabriela Beganu (2007)

RACSAM

It is well known that there were proved several necessary and sufficient conditions for the ordinary least squares estimators (OLSE) to be the best linear unbiased estimators (BLUE) of the fixed effects in general linear models. The purpose of this article is to verify one of these conditions given by Zyskind [39, 40]: there exists a matrix Q such that ΩX = XQ, where X and Ω are the design matrix and the covariance matrix, respectively. It will be shown the accessibility of this condition in some...

One singular multivariate linear model with nuisance parameters

Pavla Kunderová (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The multivariate linear model, in which the matrix of the first order parameters is divided into two matrices: to the matrix of the useful parameters and to the matrix of the nuisance parameters, is considered.

Optimal nonlinear transformations of random variables

Aldo Goia, Ernesto Salinelli (2010)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....

Outliers in models with constraints

Lubomír Kubáček (2006)

Kybernetika

Outliers in univariate and multivariate regression models with constraints are under consideration. The covariance matrix is assumed either to be known or to be known only partially.

Overview of Recent Results in Growth-curve-type Multivariate Linear Models

Ivan Žežula, Daniel Klein (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The Extended Growth Curve Model (ECGM) is a multivariate linear model connecting different multivariate regression models in sample subgroups through common variance matrix. It has the form: Y = ∑ i = 1 k X i B i Z i ' + e , vec ( e ) ∼ N n × p 0 , Σ ⊗ I n . Here, matrices X i contain subgroup division indicators, and Z i corresponding regressors. If k = 1 , we speak about (ordinary) Growth Curve Model. The model has already its age (it dates back to 1964), but it has many important applications. That is why it is still intensively studied. Many articles investigating...

Probability distribution of transformed random variables with application to nonlinear features extraction

Lubomír Soukup (1998)

Kybernetika

A method for estimation of probability distribution of transformed random variables is presented. The proposed approach admits an approximation of the transformation of the random variables. The approximate probability density function (pdf) is corrected to obtain a resulting pdf which incorporates a prior knowledge of approximation errors. The corrected pdf is not contaminated by any uncontrollable approximation. The method is applied to pattern recognition. It is shown that class conditional pdf...

Projection pursuit quadratic regression - the normal case

František Štulajter (1988)

Aplikace matematiky

The model of quadratic regression is studied by means of the projection pursuit method. This method leads to a decomposition of the matrix of quadratic regression, which can be used for an estimation of this matrix from the data observed.

Currently displaying 141 – 160 of 217