We consider a semiparametric multivariate location-scatter model where the standardized random vector of the model is fixed using simultaneously two location vectors and two scatter matrices. The approach using location and scatter functionals based on the first four moments serves as our main...

In this paper, we consider the independent component (IC) model, and the asymptotic properties of the complex valued unmixing matrix estimates that are based on simultaneous use of two scatter matrix functionals.

Statistical depth functions are being used increasingly in nonparametric multivariate data analysis. In a broad treatment of depth-based methods, Liu, Parelius, and Singh ("Multivariate analysis by date depth: Descriptive statistics, graphics and inference (with discussion)," 1999) include...

Multivariate statistical analysis relies heavily on moment assumptions of second order and higher. With increasing interest in heavy-tailed distributions, however, it is desirable to describe dispersion, skewness, and kurtosis under merely first order moment assumptions. Here, the univariate...

The median absolute deviation about the median (MAD) is an important univariate spread measure having wide appeal due to its highly robust sample version. A powerful tool in treating the asymptotics of a statistic is a linearization, i.e., a Bahadur representation. Here we establish both strong...

The median absolute deviation from the median (MAD) is an important robust univariate spread measure. It also plays important roles with multivariate data through statistics based on the univariate projections of the data, in which case a modified sample MAD introduced by Tyler [Tyler, D. E,...

This paper develops a large deviation theorem for families of sample means of U-statistic structure (i.e., U-processes). These results extend the work of Sethuraman (1964) and Wu (1994) on large deviation theory for families of ordinary sample means and the classical empirical process. Along the...