Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high dimensional setting optimal estimation of the differential entropy and the log-determinant of the covariance matrix. We first establish a central limit theore...

Abstract. This work concerns estimation of multidimensional nonlinear regression models using multilayer perceptron (MLP). The main problem with such model is that we have to know the covariance matrix of the noise to get optimal estimator. however we show that, if we choose as cost function the logarithm of the determinant of the empirical error covariance matrix, we get an asymptotically opti...

A robust multivariate quality control technique for individual observations is proposed, based on the reweighted shrinkage estimators. simulation study done to check performance and compare method with classical Hotelling approach, alternative minimum covariance determinant estimator. The results show appropriateness of even when dimension or Phase I contamination are high, both independent cor...

Mahalanobis-type distances in which the shape matrix is derived from a consistent highbreakdown robust multivariate location and scale estimator can be used to 2nd outlying points. Hardin and Rocke (http://www.cipic.ucdavis.edu/∼dmrocke/preprints.html) developed a new method for identifying outliers in a one-cluster setting using an F distribution. We extend the method to the multiple cluster c...

The minimum covariance determinant (MCD) estimator of scatter is one of the most famous robust procedures for multivariate scatter. Despite the quite important research activity related to this estimator, culminating in the recent thorough asymptotic study of Cator & Lopuhaä (2010, 2012), no results have been obtained on the corresponding estimator of shape, which is the parameter of interest i...

We consider the problem of outliers in incomplete multivariate data when the aim is to estimate a measure of mean and covariance, as is the case, for example, in factor analysis. The ER algorithm of Little and Smith which combines the EM algorithm for missing data and a robust estimation step based on an M-estimator could be used in such a situation. However, the ER algorithm as originally prop...

In modern statistics the robust estimation of parameters is a central problem, i. e., an estimation that is not or only slightly affected by outliers in the data. The Minimum Covariance Determinant estimator (MCD) [8] is probably one of the most important robust estimators of location and scatter. The complexity of computing the MCD, however, was unknown and generally thought to be exponential ...

AbstractWe propose a novel unsupervised keyphrase extraction approach that filters candidate keywords using outlier detection. It starts by training word embeddings on the target document to capture semantic regularities among words. then uses minimum covariance determinant estimator model distribution of non-keyphrase vectors, under assumption these vectors come from same distribution, indicat...

We develop a robust clustering method which unites Rousseeuw's minimum covariance determinant method and the determinant criterion of clustering analysis.