Related papers: A cautionary note on robust covariance plug-in met…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…
Co-simulation is widely used in the industry due to the emergence of modular dynamical models made up of interconnected, black-boxed systems. Several co-simulation algorithms have been developed, each with different properties and different…
The multivariate regression model basically offers the analysis of a single dataset with multiple responses. However, such a single-dataset analysis often leads to unsatisfactory results. Integrative analysis is an effective method to pool…
This article introduces a decentralized robust optimization framework for safe multi-agent control under uncertainty. Although stochastic noise has been the primary form of modeling uncertainty in such systems, these formulations might fall…
The multivariate linear regression model is an important tool for investigating relationships between several response variables and several predictor variables. The primary interest is in inference about the unknown regression coefficient…
Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between…
Maronna's and Tyler's $M$-estimators are among the most widely used robust estimators for scatter matrices. However, when the dimension of observations is relatively high, their performance can substantially deteriorate in certain…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
The global minimum-variance portfolio is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution…
Many inference techniques for multivariate data analysis assume that the rows of the data matrix are realizations of independent and identically distributed random vectors. Such an assumption will be met, for example, if the rows of the…
Three robust methods for clustering multivariate time series from the point of view of generating processes are proposed. The procedures are robust versions of a fuzzy C-means model based on: (i) estimates of the quantile cross-spectral…
We propose a new method for multivariate response regression and covariance estimation when elements of the response vector are of mixed types, for example some continuous and some discrete. Our method is based on a model which assumes the…
Biclustering is used for simultaneous clustering of the observations and variables when there is no group structure known \textit{a priori}. It is being increasingly used in bioinformatics, text analytics, etc. Previously, biclustering has…
We propose a data-driven way to reduce the noise of covariance matrices of nonstationary systems. In the case of stationary systems, asymptotic approaches were proved to converge to the optimal solutions. Such methods produce eigenvalues…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers. These can be casewise outliers, such as cases belonging to a different population, or cellwise outliers, which are deviating…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
We discuss recent work for causal inference and predictive robustness in a unifying way. The key idea relies on a notion of probabilistic invariance or stability: it opens up new insights for formulating causality as a certain risk…
In this paper, we study the convergent limits and rates of the eigenvalues and eigenvectors for spiked sample covariance matrices whose spectrum can have multiple bulk components. Our model is an extension of Johnstone's spiked covariance…