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Multivariate dynamic time series models are widely encountered in practical studies, e.g., modelling policy transmission mechanism and measuring connectedness between economic agents. To better capture the dynamics, this paper proposes a…
Relations between categorical variables can be analyzed conveniently by multiple correspondence analysis (MCA). %It is well suited to discover relations that may exist between categories of different variables. The graphical representation…
In this paper we propose a new test for the hypothesis of a constant coefficient of variation in the common nonparametric regression model. The test is based on an estimate of the $L^2$-distance between the square of the regression function…
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…
We consider the problem of detecting gradual changes in the sequence of mean functions from a not necessarily stationary functional time series. Our approach is based on the maximum deviation (calculated over a given time interval) between…
State Space Models (SSMs), particularly Mamba, have shown potential in long-term time series forecasting. However, existing Mamba-based architectures often struggle with datasets characterized by non-stationary patterns. A key observation…
We present extensive molecular dynamics simulations of the motion of a single linear rigid molecule in a two-dimensional random array of fixed obstacles. The diffusion constant for the center of mass translation, $D_{\rm CM}$, and for…
Multiple correlation is a fundamental concept with broad applications. The classical multiple correlation coefficient is developed to assess how strongly a dependent variable is associated with a linear combination of independent variables.…
The intraclass correlation coefficient (ICC) is a classical index of measurement reliability. With the advent of new and complex types of data for which the ICC is not defined, there is a need for new ways to assess reliability. To meet…
This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The proof is based on a refinement of mean-square analysis in Li…
In multi-agent systems, dynamic average consensus (DAC) is a decentralized estimation strategy in which a set of agents tracks the average of time-varying reference signals. Because DAC requires exchanging state information with neighbors,…
To solve the obscureness in measurement brought about from the weak ergodicity breaking appeared in anomalous diffusions we have suggested the time-averaged mean squared displacement (MSD) $\bar{\delta^2 (\tau)}_\tau$ with a integral…
Can a diffusion model produce its own "mental average" of a concept-one that is as sharp and realistic as a typical sample? We introduce Diffusion Mental Averages (DMA), a model-centric answer to this question. While prior methods aim to…
The log odds ratio is a well-established metric for evaluating the association between binary outcome and exposure variables. Despite its widespread use, there has been limited discussion on how to summarize the log odds ratio as a function…
This paper presents continuous dynamic average consensus (DAC) algorithms for a group of agents to estimate the average of their time-varying reference signals cooperatively. We propose consensus algorithms that are robust to agents joining…
Evaluating classifications is crucial in statistics and machine learning, as it influences decision-making across various fields, such as patient prognosis and therapy in critical conditions. The Matthews correlation coefficient (MCC) is…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
Markov chain Monte Carlo (MCMC) simulations are modeled as driven by true random numbers. We consider variance bounding Markov chains driven by a deterministic sequence of numbers. The star-discrepancy provides a measure of efficiency of…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
We consider the detection of correlated information sources in the ubiquitous Code-Division Multiple-Access (CDMA) scheme. We propose a message-passing based scheme for detecting correlated sources directly, with no need for source coding.…