Consistency of Decision in Finite and Numerable Multinomial Models

Publisher Copyright: © 2023 by the authors. This research received no external funding.The multinomial distribution is often used in modeling categorical data because it describes the probability of a random observation being assigned to one of several mutually exclusive categories. Given a finite or numerable multinomial model (Formula presented.) whose decision is indexed by a parameter (Formula presented.) and having a cost (Formula presented.) depending on (Formula presented.) and on (Formula presented.), we show that, under general conditions, the probability of taking the least cost decision tends to 1 when n tends to ∞, i.e., we showed that the cost decision is consistent, representing a Statistical Decision Theory approach to the concept of consistency, which is not much considered in the literature. Thus, under these conditions, we have consistency in the decision making. The key result is that the estimator (Formula presented.) with components (Formula presented.), where (Formula presented.) is the number of times we obtain the ith result when we have a sample of size n, is a consistent estimator of (Formula presented.). This result holds both for finite and numerable models. By this result, we were able to incorporate a more general form for consistency for the cost function of a multinomial model.publishersversionpublishe

MODELLING THE COMPROMISE MATRIX IN STATIS

STATIS methodology has three phases: Inter-structure, Compromise, and Intra-structure. In order to be able to carry out inference and simultaneously study several matched series of studies models were introduced for the first place, e. g. Areia et al. 2008 and Oliveira and Mexia 2007. In this poster we extend the models to the Compromise. We apply our approach to the results of local elections in Mainland Portugal. In the last few decades, many authors have studied a series of double-entry tables, thus originating the Join Analysis of Tables (ACT). We can considerer the STATIS methodology as na ACT method that uses Euclidian distances between configurations observed in k situations. The STATIS method was introduced by Hermier des Plantes (1976) and developed by several authors, in particular by Lavit (1988) to analyse data organized in series of studies. A study consiste of a matrix triplet (Xi, Dni, Dpi),i=1,…,k, being a data array and Dni and Dpi being two weight matrices for objects and variables. To obtain a geometrical representation of the studies, Escoufier (1976), developed the operators The compromise matrix M with diagonal matrices Dn and Dp being two weight matrices for objects and variables

Structured Stair Nesting Models-Two Approaches

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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

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Acredita(r) (n)a UCC do Alentejo: Dinamização do processo de candidatura da UCC à acreditação ACSA

Introdução: O contexto pandémico atual originou alterações sociais marcadas, propiciando ao isolamento e à diminuição da procura dos serviços de saúde por medo/ desconfiança, diminuindo a satisfação dos utentes, bem como à sobrecarga dos profissionais de saúde. Objetivo: Dinamizar o processo de Acreditação da Unidade Funcional, com o intuito de normalizar procedimentos efetuados pelos Enfermeiros da UCC, de modo a ser facilitador do desenvolvimento do seu trabalho e aumentar a satisfação dos utentes pelos cuidados recebidos. Método: Desenvolver um projeto com dupla intervenção que envolve duas comunidades (Profissionais de Saúde e Utentes), utilizando a metodologia de planeamento em saúde segundo Imperatori & Giraldes, com alicerces nos Modelos Teóricos de Avedis Donabedian sobre a Qualidade em Saúde e no Modelo de Nolah Pender sobre a promoção da saúde. Será necessário a aplicação de um questionário de satisfação à população antes e após o processo de acreditação e avaliar o impacto nesta. Resultados: Melhoria da qualidade dos cuidados de Enfermagem prestados e o aumento do grau de satisfação da população. Conclusão: Prevê-se que a Acreditação da UCC proporcione um duplo efeito, um ambiente favorável ao desempenho das funções de Enfermagem e a satisfação da população

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

Inference for types and structured families of commutative orthogonal block structures

Models with commutative orthogonal block structure, COBS, have orthogonal block structure, OBS, and their least square estimators for estimable vectors are, as it will be shown, best linear unbiased estimator, BLUE. Commutative Jordan algebras will be used to study the algebraic structure of the models and to define special types of models for which explicit expressions for the estimation of variance components are obtained. Once normality is assumed, inference using pivot variables is quite straightforward. To illustrate this class of models we will present unbalanced examples before considering families of models. When the models in a family correspond to the treatments of a base design, the family is structured. It will be shown how, under quite general conditions, the action of the factors in the base design on estimable vectors, can be studied.info:eu-repo/semantics/publishedVersio

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