Our aim is to construct a factor analysis method that can resist the effect of outliers. For this we start with a highly robust initial covariance estimator, after which the factors can be obtained from maximum likelihood or from principal factor analysis (PFA). We find that PFA based on the minimum covariance determinant scatter matrix works well. We also derive the influence function of the P...

In this paper, we propose a robust Kalman filter and smoother for the errors-invariables (EIV) state space model subject to observation noise with outliers. We introduce the EIV problem with outliers and then we present the minimum covariance determinant (MCD) estimator which is highly robust estimator to detect outliers. As a result, a new statistical test to check the existence of outliers wh...

This work studies implicitly weighted robust statistical methods suitable for econometric problems. We study robust estimation mainly for the context of heteroscedasticity or high dimension, which are up-to-date topics of current econometrics. We describe a modifi cation of linear regression resistant to heteroscedasticity and study its computational aspects. For a robust version of the instrum...

This work is concerned with the estimation of multidimensional regression and the asymp-totic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to get an optimal estimator. We show in this paper that if we choose to minimise the logarithm of the determinant of the empirical error covariance matrix, th...

In classifying high-dimensional patterns such as stellar spectra by a Gaussian classifier, the covariance matrix estimated with a small-number sample set becomes unstable, leading to degraded classification accuracy. In this paper, we investigate the covariance matrix estimation problem for small-number samples with high dimension setting based on minimum description length (MDL) principle. A n...

This work concerns the estimation of multidimensional nonlinear regression models using multilayer perceptrons (MLPs). The main problem with such models is that we need to know the covariance matrix of the noise to get an optimal estimator. However, we show in this paper that if we choose as the cost function the logarithm of the determinant of the empirical error covariance matrix, then we get...

Based on the Minimum Variance Distortionless Response-Sample Matrix Inversion (MVDRSMI) method, we propose a novel Adaptive Covariance Estimator (MVDR-ACE) beamformer for adaptation to multiple interference environments. The MVDR-ACE beamformer iteratively determines a minimum number of data samples required while maintaining its average signal-to-interference-noise to be within 3 dB from the p...

We consider a class of semi-parametric dynamic models with strong white noise errors. This processes includes the standard Vector Autoregressive (VAR) model, nonfundamental structural VAR, mixed causal-noncausal models, as well nonlinear such (multivariate) ARCH-M model. For estimation in this class, we propose Generalized Covariance (GCov) estimator, which is obtained by minimizing residual-ba...

We consider the problem of estimating, in the presence of model uncertainties, a random vector x that is observed through a linear transformation H and corrupted by additive noise. We first assume that both the covariance of x and the transformation H are not completely specified, and develop the linear estimator that minimizes the worst-case mean-squared error (MSE) across all possible covaria...

The goal of Phase I monitoring of multivariate data is to identify multivariate outliers and step changes so that the estimated control limits are sufficiently accurate for Phase II monitoring. High breakdown estimation methods based on the minimum volume ellipsoid (MVE) or the minimum covariance determinant (MCD) are well suited to detecting multivariate outliers in data. However, they are dif...