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Statistical depth functions provide measures of the outlyingness, or centrality, of the elements of a space with respect to a distribution. It is a nonparametric concept applicable to spaces of any dimension, for instance, multivariate and…

This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…

Self-supervised learning (SSL) has emerged as a powerful approach to learning representations, particularly in the field of computer vision. However, its application to dependent data, such as temporal and spatio-temporal domains, remains…

The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem. Network-based tests have the computational advantage that…

We extend generalized functional linear models under independence to a situation in which a functional covariate is related to a scalar response variable that exhibits spatial dependence-a complex yet prevalent phenomenon. For estimation,…

In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…

In analyses of rare-events, regardless of the domain of application, class-imbalance issue is intrinsic. Although the challenges are known to data experts, their explicit impact on the analytic and the decisions made based on the findings…

Functional data often arise from measurements on fine time grids and are obtained by separating an almost continuous time record into natural consecutive intervals, for example, days. The functions thus obtained form a functional time…

We introduce a method for decomposition of trend, cycle and seasonal components in spatio-temporal models and apply it to investigate the existence of climate changes in temperature and rainfall series. The method incorporates critical…

We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…

Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…

In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in…

Robust state estimation in coupled dynamical systems depends critically not only on sensor quality but on the structural alignment between observation channels and the system's intrinsic dynamics. This paper develops a rigorous framework…

Comparing yield quality distributions across multiple agricultural fields is fundamental for evaluating management practices, yet it is complicated by two pervasive data characteristics: non-normality and spatial autocorrelation.…

Structural Nested Mean Models (SNMMs) are useful for causal inference of treatment effects in longitudinal observational studies. Most existing works assume that the data are collected at pre-fixed time points for all subjects, which,…

Thousands of person-years have been invested in searches for New Physics (NP), the majority of them motivated by theoretical considerations. Yet, no evidence of beyond the Standard Model (BSM) physics has been found. This suggests that…

In this paper, we aim to improve multivariate anomaly detection (AD) by modeling the \textit{time-varying non-linear spatio-temporal correlations} found in multivariate time series data . In multivariate time series data, an anomaly may be…

We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This…

We construct a statistic and null test for examining the stationarity of time-series of discrete symbols: whether two data streams appear to originate from the same underlying unknown dynamical system, and if any difference is statistically…

We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…