Planos amostrais eficientes na estimação em modelos de mistura de escala com caudas pesadas

Abstract

In several areas of study there are several data sets that present outliers, or even significant concentrations of extreme values in the tails of their respective distributions. In the particular case of the T-Student regression, the degrees of freedom parameter is what determines the degree of robustness. The smaller the number of degrees of freedom, the more robust the tail. However, this parameter is difficult to estimate, since it is necessary to observe extreme values of the distribution. In the context of finite populations, the researcher usually does not have access to all population elements for modeling. A sampling plan must be adopted to obtain the sample. The present work proposes, in the context of superpopulation models with heavy tails and that can be described in the format of scale mixtures of normal distributions, to adopt informative sampling plans that provide a greater probability of selecting more extreme values than those that would be obtained by simple random sampling. The idea is to improve the estimation of the parametric vector associated with the thickness of the tails. Three sampling plans were proposed in the present work. For the implementation of the first, it is necessary to have an auxiliary variable, known to the entire population and related to the variable of interest. In the second, it is necessary to have knowledge of an indicator variable of the stratum to which each sample unit belongs. The simulated studies with the T-Student distribution and the study considering real data show that the sampling plans proposed provide an appreciable improvement in the estimates of the degrees of freedom parameter, both for inference under the classical and the Bayesian approaches, without great impact on the estimates of the other parameters.