  There exist multiple methods to detect outliers in multivariate data in the
literature, but most of them require to estimate the covariance matrix. The
higher the dimension, the more complex the estimation of the matrix becoming
impossible in high dimensions. In order to avoid estimating this matrix, we
propose a novel random projections-based procedure to detect outliers in
Gaussian multivariate data. It consists in projecting the data in several
one-dimensional subspaces where an appropriate univariate outlier detection
method, similar to Tukey's method but with a threshold depending on the initial
dimension and the sample size, is applied. The required number of projections
is determined using sequential analysis. Simulated and real datasets illustrate
the performance of the proposed method.
