Eficiência de estimadores robustos a observações discrepantes em modelo de regressão multivariada com aplicação na análise sensorial do café

Abstract

Given the sensibility of the least squares method to the outliers presence it is known that the estimates of least squares are affected by the presence of one or more of those observations. This way, the objective of this work was to search the effect of outliers in the adjustment of models of multivariate regression. With this purpose, efficiency measures among robust estimators Minimum Covariance Determinant - MCD and Minimum Volume Ellipsoid - MVE were used in simulation Monte Carlo considering distributions to present deviations symmetry and excess kurtosis in relation to the multivariate normal distribution. In this context, a new measure was proposed and its validation made by simulation studies Monte Carlo, assuming different parametric configurations specified by structure of the covariance matrix, number of variables and sample size. After the validation of the estimators, multivariate regression models were adjusted considering variables concerning the sensorial and chemical profile of genotypes of arabica coffee (Coffea arabica L.). The relative results to the simulation indicated that MVE estimator was more efficient when the effect of the observations came from distributions with deviation symmetry and excess kurtosis. About the application, the regression models adjusted to the MCD and MVE methods were more appropriate for the study of the physiochemical and sensory variables, being consistent with the experimental results.