Statistics

For hypothesis testing of functional parameters, given a functional statistic $T_n$ and a functional depth $D$ with respect to the distribution $P_n$ of $T_n$, we propose the depth value $DT_n \equiv D(T_n;P_n)$ as a test statistic, which…

Detecting structural instability and anomalies in high-dimensional financial time series is challenging due to complex temporal dependence and evolving cross-sectional structure. We propose ReGEN-TAD, an interpretable generative framework…

In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction…

Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…

Bayesian hierarchical models fit to complex survey data require variance correction for the sampling design, yet applying this correction uniformly harms parameters already protected by the hierarchical structure. We propose the Design…

The Galton board is a well known device for showing how repeated Bernoulli trials on a triangular lattice produce an approximately normal distribution. Marking the 150th anniversary of Galton's 1875 construction, this paper revisits the…

Longitudinal data analysis is fundamental for understanding dynamic processes in biomedical and social sciences. Although varying coefficient models (VCMs) provide a flexible framework by allowing covariate effects to evolve over time,…

Granger causality (GC), a popular statistical method for the inference of directional influences between time series measured from a complex network, is sensitive to high-order (non-pairwise) interactions which fundamentally shape the…

In this paper, we address a fundamental limitation of the classical Wasserstein barycenter -- its sensitivity to outliers and its reliance on finite first/second moment assumptions. To overcome these issues, we propose the robust…

We develop an efficient posterior sampling scheme for the Poisson INGARCH models. The proposed method is based on the approximation of the posterior density that exploits the Poisson limit of the negative binomial distribution. It allows us…

Privacy protection and uncertainty quantification are increasingly important in data-driven decision making. Conformal prediction provides finite-sample marginal coverage, but existing private approaches often rely on data splitting,…

While the traditional goal of statistics is to infer population parameters, modern practice increasingly demands protection of individual privacy. One way to address this need is to adapt classical statistical procedures into…

Linear mixed-effects model (LMM) is a cornerstone of longitudinal data analysis, but is limited to adeptly make heterogeneous analyses predictable under both group-specific fixed effects and subject-specific random effects. To address this…

As buildings become increasingly connected and sensor-rich, intelligent remote heating control is rapidly superseding conventional local heating control. Such control algorithms often aim at reducing energy consumption by minimizing…

This monograph provides a rigorous overview of theoretical and methodological aspects of probabilistic inference and learning with Stein's method. Recipes are provided for constructing Stein discrepancies from Stein operators and Stein…

Nonparametric density estimation for compositional data supported on the simplex is examined under a missing at random mechanism. Rather than imputing missing values and estimating the density from a completed data set, we adopt a strategy…

Measurement error is prevalent across all domains of scientific research where only imprecise observations, rather than the true underlying values, can be obtained. For example, estimates of human microbiome diversity are based on small…

Censoring high-motion volumes in fMRI is common practice to reduce effects of head motion on functional connectivity (FC). Although aggressive censoring removes more noise, it causes extensive data loss, creating a tradeoff that may…

We introduce a repulsive mixture model to cluster observation units represented by multivariate functional data, based on similarity of curve shapes and individual-specific covariates. We propose a repulsive prior distribution for the…

We prove a general result that if a Metropolis--Hastings algorithm has a proposal that is not geometrically ergodic and the acceptance rate approaches unity at a suitable rate as the state variable becomes large, then the Metropolised chain…