Estimation in mixed models through three step minimization

The aim of this article is to present an estimation procedure for both fixed effects and variance components in linear mixed models. This procedure consists of a maximum likelihood method which we call Three Step Minimization, TSM. The major contribution of this method is that when variances tend to be null standard algorithms behave badly, unlike the TSM method, which uses a grid search algorithm in a compact set. A numerical application with real and simulated data is provided.info:eu-repo/semantics/publishedVersio

Limit distributions for asymptotically linear statistics with spherical error

The aim of this work is to obtain general results for the limit distributions of asymptotically linear statistics when the error is spherical, increasing non-centrality. These results apply directly to homoscedastic normal error thus to high precision measurements. We present a numerical example on cylinder volume to illustrate the usefulness of our approach.info:eu-repo/semantics/publishedVersio

Tests and relevancies for the hypotheses of an orthogonal family in a model with orthogonal block structure

A model has an orthogonal block structure if it has, as covariance matrix, a linear combination of pairwise orthogonal projection matrices, that add up to the iden- tity matrix. The range space of these matrices are associated to hypotheses of an orthogonal family. In this paper we show how to obtain tests for these hypotheses when normality is assumed and how to consider their relevance when normality is discarded. Besides the notion of relevance, we formulate hypotheses in a general way that may be applied to models with orthogonal block structure, whose factors may have xed and/or random e ects. The results are applied to prime basis factorial models and an example is presented.info:eu-repo/semantics/publishedVersio

One-way random effects ANOVA with random sample sizes: An application to a Brazilian database on cancer registries

ANOVA is routinely used in many situations, namely in medical research, where the sample sizes may not be previously known. This leads us to consider the samples sizes as realizations of random variables. The aim of this paper is to extend one-way random effects ANOVA to those situations and apply our results to a Brazilian database on cancer registries.info:eu-repo/semantics/publishedVersio

One-way fixed effects ANOVA with missing observations

The aim of this paper is to extend the theory of F-tests with random sample sizes to situations when missing observations may occur. We consider the one-way ANOVA with fixed effects. This approach is illustrated through an application to patients affected by melanoma skin cancer, from three different states of Brazil.info:eu-repo/semantics/publishedVersio

Estimation in additive models and ANOVA-like applications

A well-known property of cumulant generating function is used to estimate the first four order cumulants, using least-squares estimators. In the case of additive models, empirical best linear unbiased predictors are also obtained. Pairs of independent and identically distributed models associated with the treatments of a base design are used to obtain unbiased estimators for the fourth-order cumulants. An application to real data is presented, showing the good behaviour of the least-squares estimators and the great flexibility of our approach.info:eu-repo/semantics/publishedVersio

Estimation and Orthogonal Block Structure

Estimators with good behaviors for estimable vectors and variance components are obtained for a class of models that contains the well known models with orthogonal block structure, OBS, see [15], [16] and [1], [2]. The study observations of these estimators uses commutative Jordan Algebras, CJA, and extends the one given for a more restricted class of models, the models with commutative orthogonal block structure, COBS, in which the orthogonal projection matrix on the space spanned by the means vector commute with all variance-covariance matrices, see [7].info:eu-repo/semantics/publishedVersio

Chisquared and related inducing pivot variables: an application to orthogonal mixed models

We use chi-squared and related pivot variables to induce probability measures for model parameters, obtaining some results that will be useful on the induced densities. As illustration we considered mixed models with balanced cross nesting and used the algebraic structure to derive confidence intervals for the variance components. A numerical application is presented.info:eu-repo/semantics/publishedVersio

Considering the sample sizes as truncated Poisson random variables in mixed effects models

When applying analysis of variance, the sample sizes may not be previously known, so it is more appropriate to consider them as realizations of random variables. A motivating example is the collection of observations during a fixed time span in a study comparing, for example, several pathologies of patients arriving at a hospital. This paper extends the theory of analysis of variance to those situations considering mixed effects models. We will assume that the occurrences of observations correspond to a counting process and the sample dimensions have Poisson distribution. The proposed approach is applied to a study of cancer patients.info:eu-repo/semantics/publishedVersio

Estimation and incommutativity in mixed models

In this paper we present a treatment for the estimation of variance components and estimable vectors in linear mixed models in which the relation matrices may not commute. To overcome this difficulty, we partition the mixed model in sub-models using orthogonal matrices. In addition, we obtain confidence regions and derive tests of hypothesis for the variance components. A numerical example is included. There we illustrate the estimation of the variance components using our treatment and compare the obtained estimates with the ones obtained by the ANOVA method. Besides this, we also present the restricted and unrestricted maximum likelihood estimates.info:eu-repo/semantics/publishedVersio