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This article explores U-Statistics as a tool for testing conditional correlation between two multivariate sources with respect to a potential confounder. The proposed approach is effectively an instance of weighted U-Statistics and does not impose any statistical model on the processed data, in contrast to other well-known techniques that assume Gaussianity. By avoiding determinants and inverses, the method presented displays promising robustness in small-sample regimes. Its performance is evaluated numerically through its MSE and ROC curves.

We propose a numerical methodology for detecting periodicities in unknown colored noise and for evaluating the ‘significance levels’ (p-values) of the test statistics. The procedure assumes and leverages the existence of a set of time series obtained under the null hypothesis (a null training sample, NTS) and possibly complementary side information. The test statistic is computed from a standardized periodogram, which is a pointwise division of the periodogram of the series under test to an averaged periodogram obtained from the NTS.

In many practical parameter estimation problems,
such as coefficient estimation of polynomial regression, the true
model is unknown and thus, a model selection step is performed
prior to estimation. The data-based model selection step affects
the subsequent estimation. In particular, the oracle Cramér-Rao
bound (CRB), which is based on knowledge of the true model, is
inappropriate for post-model-selection performance analysis and
system design outside the asymptotic region. In this paper, we

Graphs are fundamental mathematical structures used in various fields to model statistical and physical relationships between data, signals, and processes. In some applications, such as data processing in graphs that represent physical networks, the initial network topology is known. However, disconnections of edges in the network change the topology and may affect the signals and processes over the network. In this paper, we consider the problem of edge disconnection identification in networks by using concepts from graph signal processing.

Particle filtering is used to compute nonlinear estimates of complex systems. It samples trajectories from a chosen distribution and computes the estimate as a weighted average of them. Easy-to-sample distributions often lead to degenerate samples where only one trajectory carries all the weight, negatively affecting the resulting performance of the estimate. While much research has been done on the design of appropriate sampling distributions that would lead to controlled degeneracy, in this paper our objective is to learn sampling distributions.