Proposição de testes robustos comedian para detecção de outliers multivariados baseados em resíduos da análise de componentes principais

Abstract

In various studies, random samples of univariate or multivariate variables are encountered. In many cases, the presence of observations referred to as outliers is responsible for significant compromises in statistical inference. Detecting outliers becomes extremely important in these cases, as the inferences made can lead to incorrect conclusions. In a multivariate dataset, the detection of outliers is more complex than in univariate cases because the dimension is defined beyond the real line. There are tests for detecting multivariate outliers. All of them depend on

asymptotic and normal distributions and are highly influenced by the presence of the very ou- tliers they aim to identify and exclude from the random sample. In this context, the objective of

this study was to propose robust asymptotic tests based on the comedian estimator and residu- als from principal component analysis to detect multivariate outliers. It also aimed to compare

the performance of the proposed tests with existing tests evaluated in this study through Monte Carlo simulation, measuring the tests’ ability to identify outliers and non-outliers in the random sample. For the generation of simulated data, a sample from a multivariate normal population was used. From the sample data, principal components were obtained for conducting the tests using the R software. The existing tests are those of Jackson and Mudholkar and Rao. The proposed tests consist of the Jackson and Mudholkar test and the Rao test, both using the robust comedian estimator. It was concluded that the proposed tests, utilizing the robust comedian estimator, achieved the best results in detecting outliers. Furthermore, the Rao test, when using the comedian estimator, stood out as the best, as it also correctly identified non-outliers.