RT info:eu-repo/semantics/article
T1 Consistency factor for the MCD estimator at the Student-t distribution
A1 García Escudero, Luis Ángel
A1 Mayo Iscar, Agustín
A1 Cerioli, Andrea
A1 Barabesi, Lucio
K1 Consistency factor
K1 MCD
K1 Robust distance
K1 Multivariate
K1 Student-t distribution
AB It is well known that trimmed estimators of multivariate scatter, such as the Minimum Covariance Determinant (MCD) estimator, are inconsistent unless an appropriate factor is applied to them in order to take the effect of trimming into account. This factor is widely recommended and applied when uncontaminated data are assumed to come from a multivariate normal model. We address the problem of computing a consistency factor for the MCD estimator in a heavy-tail scenario, when uncontaminated data come from a multivariate Student-t distribution.We derive a remarkably simple computational formula for the appropriate factor and show that it reduces to an even simpler analytic expression in the bivariate  case. Exploiting our formula, we then develop a robust Monte Carlo procedure for estimating the usually unknown number of degrees of freedom of the assumed and possibly contaminated multivariate Student-t model, which is a necessary ingredient for obtaining the required consistency factor. Finally, we provide substantial simulation evidence about the proposed procedure and apply it to data from image processing and financial markets.
SN 0960-3174
YR 2023
FD 2023
LK https://uvadoc.uva.es/handle/10324/67296
UL https://uvadoc.uva.es/handle/10324/67296
LA eng
NO Statistics and Computing (2023) 33:132, 1-17
NO Producción Científica
DS UVaDOC
RD 24-dic-2024