Related papers: A Robust Moment System Based on Absolute Deviation…

In astronomical observations, the estimation of distances from parallaxes is a challenging task due to the inherent measurement errors and the non-linear relationship between the parallax and the distance. This study leverages ideas from…

State-space models are pivotal for dynamic system analysis but often struggle with outlier data that deviates from Gaussian distributions, frequently exhibiting skewness and heavy tails. This paper introduces a robust extension utilizing…

There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…

Out-of-distribution (OOD) robustness is a critical challenge for modern machine learning systems, particularly as they increasingly operate in multimodal settings involving inputs like video, audio, and sensor data. Currently, many OOD…

Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…

Empirical researchers often trim observations with small denominator A when they estimate moments of the form E[B/A]. Large trimming is a common practice to mitigate variance, but it incurs large trimming bias. This paper provides a novel…

This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…

This paper introduces a robust and computationally efficient estimation framework for high-dimensional volatility models in the BEKK-ARCH class. The proposed approach employs data truncation to ensure robustness against heavy-tailed…

We consider the problem of sparsity-constrained $M$-estimation when both explanatory and response variables have heavy tails (bounded 4-th moments), or a fraction of arbitrary corruptions. We focus on the $k$-sparse, high-dimensional regime…

A new lifetime model, named the Modi linear failure rate distribution, is suggested. This flexible model is capable of accommodating a wide range of hazard rate shapes, including decreasing, increasing, bathtub, upside-down bathtub, and…

For many inference problems in statistics and econometrics, the unknown parameter is identified by a set of moment conditions. A generic method of solving moment conditions is the Generalized Method of Moments (GMM). However, classical GMM…

Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to…

Medical multi-modal learning is critical for integrating information from a large set of diverse modalities. However, when leveraging a high number of modalities in real clinical applications, it is often impractical to obtain full-modality…

The Maximum Mean Discrepancy (MMD) is a widely used multivariate distance metric for two-sample testing. The standard MMD test statistic has an intractable null distribution typically requiring costly resampling or permutation approaches…

The q-Gaussians are a class of stable distributions which are present in many scientific fields, and that behave as heavy tailed distributions for an especific range of q values. The identification of these values, which are used in the…

Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…

We extend the class of tempered stable distributions first introduced in Rosinski 2007. Our new class allows for more structure and more variety of tail behaviors. We discuss various subclasses and the relation between them. To characterize…

With the widespread availability of sensor data across industrial and operational systems, we frequently encounter heterogeneous time series from multiple systems. Anomaly detection is crucial for such systems to facilitate predictive…

We study algorithms for online change-point detection (OCPD), where samples that are potentially heavy-tailed, are presented one at a time and a change in the underlying mean must be detected as early as possible. We present an algorithm…

We leverage recent advances in heavy-tail approximations for global hypothesis testing with dependent studies to construct approximate confidence regions without modeling or estimating their dependence structures. A non-rejection region is…