Observações atípicas em alta dimensão

Abstract

Outliers and heteroskedastic noise are two common situations in Statistics. Nowadays the amount of generated data is very high and for this reason it is possible to find high dimensional data (the dimension d is just as large or larger than the number of observations n). Furthermore, it is possible that the data have heteroskedastic noise, which means that the noise variance can be different entrywise. Principal component analysis is a technique that aims to create a subspace with lower dimension than the original space. The technique is used in different areas such as Statistics, Econometrics, Machine Learning and Applied Mathematics. Choi and Marron (2019) introduced a new notion of high dimensional outliers that embraces other types and also investigates the behaviour of these outliers in the subspace created by the principal components analysis. Most of the techniques used in this context are based on the assumption of homoskedastic noise. However, as mentioned before, it is known that this is not always the case. Therefore, Zhang, Cai and Wu (2022) proposed a new method called HeteroPCA, which main objective is to remove the bias of the main diagonal of the sample covariance matrix due to heteroskedasticity. In this work, the main objective is to combine the method proposed by Zhang, Cai and Wu (2022) and the methodology proposed by Choi and Marron (2019) to find a subspace capable of identifying the presence of outliers when heteroskedasticity noise is present.