Propriedades e aspectos geométricos de estimadores tipo James-Stein e do estimador de Hartigan

The James-Stein estimator is a biased shrinkage estimator with uniformly smaller risk than the risk of the sample mean estimator for the mean of multivariate normal distribution, except in the one-dimensional or two-dimensional cases. In this work we have used more heuristic arguments and intensified the geometric treatment of the theory of James-Stein estimator. New type James-Stein shrinking estimators are proposed and the Mahalanobis metric used to address the James-Stein estimator. . To evaluate the performance of the estimator proposed, in relation to the sample mean estimator, we used the computer simulation by the Monte Carlo method by calculating the mean square error. The result indicates that the new estimator has better performance relative to the sample mean estimator.

Análise de experimentos fatoriais de dois fatores com tratamentos adicionais

Experiments using factorial arrangement of treatments are rather common and useful in agricultural research. The main advantage is the possibility of testing many hypotheses, allowing broader conclusions over different factors, studied simultaneously. Factorial arrangements are used to compare levels of each factor (main effects), and also to verify if the differences among levels of a given factor are dependent on the levels of the other factors (interacions). In the analysis of data from factorial experiments, difficulty is increased when additional treatments are included. Inclusion of one or more additional treatments is a quite common practice, since such treatments are usually taken as reference or standard for evaluation and comparasion of the remaimng treatments, or aiming complementary information. This increase of difficulty is however low, compared to the advantages. As in literature there are few references about the statistical analysis of factorial experiments with additonal treatments, and given straightforward use in experimentation, the objective of this work was the presentation of approach for the use of factorial experiments with additonal treatments trough the analysis of some examples using the SAS® software, with the corresponding theoretical development, obtaining the system of normal equations, estimators of the parameters and variance of contrasts among two treatment means. It is suggested that additional treatments should be used with caution. The analysis of variance of such kind of experiment was presented using matrix notation.