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Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the…
Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…
Regression adjustments are often considered by investigators to improve the estimation efficiency of causal effect in randomized experiments when there exists many pre-experiment covariates. In this paper, we provide conditions that…
We give answer to an open problem regarding consistency of the maximum likelihood estimators (MLEs) in generalized linear mixed models (GLMMs) involving crossed random effects. The solution to the open problem introduces an interesting,…
Models with multiple change points are used in many fields; however, the theoretical properties of maximum likelihood estimators of such models have received relatively little attention. The goal of this paper is to establish the asymptotic…
Choosing models from a hypothesis space is a frequent task in approximation theory and inverse problems. Cross-validation is a classical tool in the learner's repertoire to compare the goodness of fit for different reconstruction models.…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
In many complex statistical models maximum likelihood estimators cannot be calculated. In the paper we solve this problem using Markov chain Monte Carlo approximation of the true likelihood. In the main result we prove asymptotic normality…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions.…
New asymptotic approximations of the non-central $t$ distribution are given, a generalization of the Student's $t$ distribution. Using new integral representations, we give new asymptotic expansions for large values of the noncentrality…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point…
We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
The aim of this note is to announce some results about the probabilistic and deterministic asymptotic properties of linear groups. The first one is the analogue, for norms of random matrix products, of the classical theorem of Cramer on…
This paper provides a selective review of the statistical network analysis literature focused on clustering and inference problems for stochastic blockmodels and their variants. We survey asymptotic normality results for stochastic…