A Distribution-Free $M$-Estimator of Multivariate Scatter

A Multivariate Hill Estimator

We propose a simple and semi-parametric estimator for the tail index of a regular varying elliptical random vector. Since, for univariate random variables, our estimator boils down to the Hill estimator and it inherits the simplicity and asymptotic properties, we name it after Bruce M. Hill. The estimator is based on the distance between an elliptical probability contour and the outer – or exce...

A Distribution-Free Multivariate Control Chart

Monitoring multivariate quality variables or data streams remains an important and challenging problem in statistical process control (SPC). Although the multivariate SPC has been extensively studied in the literature, designing distribution-free control schemes are still challenging and yet to be addressed well. This paper develops a new nonparametric methodology for monitoring location parame...

Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter

The Forward Search is a powerful general method for detecting anomalies in structured data, whose diagnostic power has been shown in many statistical contexts. However, despite the wealth of empirical evidence in favour of the method, only few theoretical properties have been established regarding the resulting estimators. We show that the Forward Search estimators are strongly consistent at th...

Multivariate normal distribution - Wikipedia, the free encyclopedia

1 General case 1.1 Cumulative distribution function 1.2 A counterexample 1.3 Normally distributed and independent 2 Bivariate case 3 Affine transformation 4 Geometric interpretation 5 Correlations and independence 6 Higher moments 7 Conditional distributions 8 Fisher information matrix 9 Kullback-Leibler divergence 10 Estimation of parameters 11 Entropy 12 Multivariate normality tests 13 Drawin...

Screening for a Multivariate Mixture Normal Distribution