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We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…

Statistics Theory · Mathematics 2013-01-23 Georgios Fellouris , Alexander G. Tartakovsky

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…

Statistics Theory · Mathematics 2013-10-30 Peter Bickel , David Choi , Xiangyu Chang , Hai Zhang

In this paper, the Neyman-Pearson lemma for general sublinear expectations is studied. We weaken the assumptions for sublinear expectations in [1] and give a completely new method to study this problem. Applying Mazur-Orlicz Theorem and the…

Probability · Mathematics 2021-08-31 Chuanfeng Sun , Shaolin Ji

This paper proposes a local projection residual bootstrap method to construct confidence intervals for impulse response coefficients of AR(1) models. Our bootstrap method is based on the local projection (LP) approach and involves a…

Econometrics · Economics 2026-01-14 Amilcar Velez

This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…

Statistics Theory · Mathematics 2016-06-06 W. T. M. Dunsmuir , J. Y. He

Let $\bigl\{X_k\bigr\}_{k \in \mathbb{Z}} \in \mathbb{L}^2(\mathcal{T})$ be a stationary process with associated lag operators ${\boldsymbol{\cal C}}_h$. Uniform asymptotic expansions of the corresponding empirical eigenvalues and…

Statistics Theory · Mathematics 2016-02-16 Moritz Jirak

We define the group-lasso estimator for the natural parameters of the exponential families of distributions representing hierarchical log-linear models under multinomial sampling scheme. Such estimator arises as the solution of a convex…

Statistics Theory · Mathematics 2012-07-31 Yuval Nardi , Alessandro Rinaldo

The statistical analysis of Randomized Numerical Linear Algebra (RandNLA) algorithms within the past few years has mostly focused on their performance as point estimators. However, this is insufficient for conducting statistical inference,…

Statistics Theory · Mathematics 2020-02-26 Ping Ma , Xinlian Zhang , Xin Xing , Jingyi Ma , Michael W. Mahoney

We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…

Optimization and Control · Mathematics 2024-05-15 Joshua Cutler , Mateo Díaz , Dmitriy Drusvyatskiy

We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…

Statistics Theory · Mathematics 2026-02-20 Alhad Sethi , Kavali Sofia Sagar , Shubhada Agrawal , Debabrota Basu , P. N. Karthik

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic…

Statistics Theory · Mathematics 2014-03-12 Kyungchul Song

Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…

Statistics Theory · Mathematics 2025-10-17 Amaze Lusompa

Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio…

Statistics Theory · Mathematics 2007-06-13 Jianqing Fan , Jian Zhang

Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate…

Statistics Theory · Mathematics 2009-01-09 Jean-Marc Bardet , Olivier Wintenberger

Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…

Machine Learning · Statistics 2026-05-12 Valentin Kilian , Stefano Cortinovis , François Caron

In this note, we propose a new approach for the proof of the consistency and normality of the maximum likelihood estimator for nonlinear AR processes with markov-switching under the assumptions of uniform exponential forgetting of the…

Statistics Theory · Mathematics 2016-06-01 Luis-Angel Rodríguez

Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…

Statistics Theory · Mathematics 2011-03-29 Thomas A. Dean , Sumeetpal S. Singh , Ajay Jasra , Gareth W. Peters

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

Statistics Theory · Mathematics 2024-05-16 Lucas Reding , Andrés F. López-Lopera , François Bachoc

Low Ambiguity Zone (LAZ) sequences play a pivotal role in modern integrated sensing and communication (ISAC) systems. Recently, Wang \textit{et al.} [arXiv:2501.11313] proposed a definition of locally perfect nonlinear functions (LPNFs) and…

Information Theory · Computer Science 2025-08-12 Zhiye Yang , Zheng Wang , Huaning Liu , Keqin Feng

We discuss the optimal design problem in regression models with long-range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these designs depend only indirectly on the correlation function.…

Statistics Theory · Mathematics 2012-05-15 Holger Dette , Nikolai Leonenko , Andrey Pepelyshev , Anatoly Zhigljavsky