In High Dimension, Low Sample Size (HDLSS) data situations, where the dimension d is much larger than the sample size n, principal component analysis (PCA) plays an important role in statistical analysis. Under which conditions does the sample PCA well reflect the population covariance structure? We answer this question in a relevant asymptotic context where d grows and n is fixed, under a gene...

A lot is known about the Hölder regularity of stochastic processes, in particular in the case of Gaussian processes. Recently, a finer analysis of the local regularity of functions, termed 2-microlocal analysis, has been introduced in a de-terministic frame: through the computation of the so-called 2-microlocal frontier, it allows in particular to predict the evolution of regularity under the a...

In this paper, a co-prime symmetric sparse cross array is employed to estimate twodimensional (2-D) direction-of-arrival (DOA). Some special forth-order-cumulants (FOCs) of array received data are used to construct a high-order matrix that is equivalent to a cross-covariance matrix based on two uniform linear arrays. After some modifications, an existing 2-D DOA estimation algorithm becomes mor...

The time relationships which characterize intermedia synchronization in a multimedia stream affect network performance. In this paper an analytical framework is presented in order to model the multimedia traffic and to evaluate the performance of a multiplexer loaded by multimedia sources. The emission process of each multimedia source is defined as the superposition of heterogeneous correlated...

Partial Least Squares (PLS) is a statistical technique that is widely used in the Partial Least Squares (PLS) is a popular technique for estimating structural equation models with latent variables. It is frequently perceived as an alternative to covariance analysis of such models. While its proponents recognize the shortcomings of PLS for testing explanatory models in comparison to covariance m...

In classical mechanics, Galilean covariance and the principle of relativity are completely equivalent and hold for all possible dynamical processes. In contrast, in relativistic physics the situation is much more complex. It will be shown that Lorentz covariance and the principle of relativity are not completely equivalent. The reason is that the principle of relativity actually only holds for ...

This paper addresses the problem of estimating the covariance matrix reliably when the assumptions, such as Gaussianity, on the probabilistic nature of multichannel data do not necessarily hold. Multivariate spatial sign and rank functions, which are generalizations of univariate sign and centered rank, are introduced. Furthermore, spatial rank covariance matrix and spatial Kendall’s tau covari...

J. R. Ristorcelli X Division, Los Alamos National Laboratory University of California, Los Alamos, NM 87545 A.C. Poje Division of Applied Mathematics Brown University, Providence, RI 02192 Abstract The e ects of Rossby wave { turbulence interactions on particle dispersion are investigated in a Lagrangian analysis of the potential vorticity equation. The analysis produces several exact statistic...

Interpolation techniques play a central role in Astronomy, where one often needs to smooth irregularly sampled data into a smooth map. In a previous article (2001AA...373..359L, hereafter Paper I), we have considered a widely used smoothing technique and we have evaluated the expectation value of the smoothed map under a number of natural hypotheses. Here we proceed further on this analysis and...