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We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…

Statistics Theory · Mathematics 2026-03-06 Jingyu Liu , Yanglei Song

In this paper we consider two closely related problems : estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and…

Statistics Theory · Mathematics 2008-05-06 Debashis Paul , Jie Peng

This work considers parameter estimation for Gaussian process interpolation with a periodized version of the Mat{\'e}rn covariance function introduced by Stein. Convergence rates are studied for the joint maximum likelihood estimation of…

Statistics Theory · Mathematics 2025-05-20 Sébastien J Petit

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…

Econometrics · Economics 2025-09-16 Jiatong Li , Hongqiang Yan

Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…

Computational Engineering, Finance, and Science · Computer Science 2023-12-14 Maximilian Dinkel , Carolin M. Geitner , Gil Robalo Rei , Jonas Nitzler , Wolfgang A. Wall

In this paper, we provide explicit formulas, in terms of the covariances of sample covariances or sample correlations, for the asymptotic covariances of unrotated factor loading estimates and unique variance estimates. These estimates are…

Statistics Theory · Mathematics 2018-11-14 Xingwei Hu

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…

Machine Learning · Statistics 2018-11-06 Edwin V. Bonilla , Karl Krauth , Amir Dezfouli

Maximum Likelihood (ML) estimation requires precise knowledge of the underlying statistical model. In Quasi ML (QML), a presumed model is used as a substitute to the (unknown) true model. In the context of Independent Vector Analysis (IVA),…

Signal Processing · Electrical Eng. & Systems 2020-09-01 Amir Weiss , Sher Ali Cheema , Martin Haardt , Arie Yeredor

This paper provides a precise error analysis for the maximum likelihood estimate $\hat{a}_{\text{ML}}(u_1^n)$ of the parameter $a$ given samples $u_1^n = (u_1, \ldots, u_n)'$ drawn from a nonstationary Gauss-Markov process $U_i = a U_{i-1}…

Information Theory · Computer Science 2021-03-29 Peida Tian , Victoria Kostina

Drees and Rootz\'en (2010) have established limit theorems for a general class of empirical processes of statistics that are useful for the extreme value analysis of time series, but do not apply to statistics of sliding blocks, including…

Statistics Theory · Mathematics 2020-09-02 Holger Drees , Sebastian Neblung

We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[{}_2F_1(a+\epsilon\lambda,b;c+\lambda;x),\qquad 0<x<1\] as $\lambda\to+\infty$ in the neigbourhood of $\epsilon x=1$ when the parameter $\epsilon>1$ and…

Classical Analysis and ODEs · Mathematics 2021-04-27 R. B. Paris

Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…

Statistics Theory · Mathematics 2015-03-17 Piet Groeneboom , Geurt Jongbloed

McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over…

Machine Learning · Statistics 2014-06-23 Alexander G. de. G Matthews , Zoubin Ghahramani

These notes were written for the mini-course "Extrema of log-correlated random variables: Principles and Examples" at the Introductory School held in January 2015 at the Centre International de Rencontres Math\'ematiques in Marseille. There…

Probability · Mathematics 2016-01-05 Louis-Pierre Arguin

We establish the asymptotic distribution of likelihood ratio tests (LRTs) in settings where some of the nuisance parameters are unidentifiable under the null hypothesis, parameters of interest lie on the boundary of the parameter space, and…

Statistics Theory · Mathematics 2026-05-13 Karl Oskar Ekvall , Ola Hössjer , Matteo Bottai , J. M. Patrik Albin

We study the persistence probabilities of a moving average process of order one with uniform innovations. We identify a number of regions, characterized by the location of the uniform distribution and the coupling parameter of the process,…

Probability · Mathematics 2025-07-08 Frank Aurzada , Kilian Raschel

Let $\{X_i(t),t\ge0\}, 1\le i\le n$ be independent centered stationary Gaussian processes with unit variance and almost surely continuous sample paths. For given positive constants $u,T$, define the set of conjunctions $C_{[0,T],u}:=\{t\in…

Probability · Mathematics 2014-10-08 Krzysztof Dȩbicki , Enkelejd Hashorva , Lanpeng Ji , Kamil Tabis

Roy's largest root is a common test statistic in multivariate analysis, statistical signal processing and allied fields. Despite its ubiquity, provision of accurate and tractable approximations to its distribution under the alternative has…

Statistics Theory · Mathematics 2015-07-06 Iain M. Johnstone , Boaz Nadler

In this paper, a unified approach is proposed to derive the exact local asymptotic power for panel unit root tests, which is one of the most important issues in nonstationary panel data literature. Two most widely used panel unit root tests…

Econometrics · Economics 2017-10-10 Zhongwen Liang

The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…

Statistics Theory · Mathematics 2009-09-29 Moulinath Banerjee