统计理论
We introduce isotonic conditional laws (ICL) which extend the classical notion of conditional laws by the additional requirement that there exists an isotonic relationship between the random variable of interest and the conditioning random…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
For exponentially distributed lifetimes, we consider the prediction of future order statistics based on having observed the first $m$ order statistics. We focus on the previously less explored aspects of predicting: (i) an arbitrary pair of…
Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in…
Constructing distribution-free confidence intervals for the median, a classic problem in statistics, has seen numerous solutions in the literature. While coverage validity has received ample attention, less has been explored about interval…
The $\beta$-model has been extensively utilized to model degree heterogeneity in networks, wherein each node is assigned a unique parameter. In this article, we consider the hypothesis testing problem that two nodes $i$ and $j$ of a…
Semi-supervised datasets are ubiquitous across diverse domains where obtaining fully labeled data is costly or time-consuming. The prevalence of such datasets has consistently driven the demand for new tools and methods that exploit the…
We consider the graphon mean-field system introduced in the work of Bayraktar, Chakraborty, and Wu. It is the large-population limit of a heterogeneously interacting diffusive particle system, where the interaction is of mean-field type…
This study investigates the experimental design problem for identifying the arm with the highest expected outcome, referred to as best arm identification (BAI). In our experiments, the number of treatment-allocation rounds is fixed. During…
Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This…
We propose a new approach for sampling and Bayesian computation that uses the score of the target distribution to construct a transport from a given reference distribution to the target. Our approach is an infinite-dimensional Newton…
Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…
In this paper, we explore adaptive inference based on variational Bayes. Although several studies have been conducted to analyze the contraction properties of variational posteriors, there is still a lack of a general and computationally…
Varimax factor rotations, while popular among practitioners in psychology and statistics since being introduced by H. Kaiser, have historically been viewed with skepticism and suspicion by some theoreticians and mathematical statisticians.…
In this paper, we focus on the BDS test, which is a nonparametric test of independence. Specifically, the null hypothesis $H_{0}$ of it is that $\{u_{t}\}$ is i.i.d. (independent and identically distributed), where $\{u_{t}\}$ is a random…
We do the error analysis in reliability measures due to the assumption of independence amongst the component lifetimes. In reliability theory, we come across different n-component structures like series, parallel, and k-out-of-n systems. A…
We define an asymptotically normal wavelet-based strongly consistent estimator for the Hurst parameter of any Hermite processes. This estimator is obtained by considering a modified wavelet variation in which coefficients are wisely chosen…
Consider the problem of binary hypothesis testing. Given $Z$ coming from either $\mathbb P^{\otimes m}$ or $\mathbb Q^{\otimes m}$, to decide between the two with small probability of error it is sufficient, and in many cases necessary, to…
We consider the problem of forecasting multivariate time series by a Seemingly Unrelated Time Series Equations (SUTSE) model. The SUTSE model usually assumes that error variables are correlated. A crucial issue is that the model estimation…
The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix…