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In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…

Statistics Theory · Mathematics 2020-05-26 Rodrigo A. González , Cristian R. Rojas

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…

Machine Learning · Computer Science 2016-09-13 Steve Hanneke

In this paper we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over an linearly…

Optimization and Control · Mathematics 2023-03-07 Christoph Mark , Steven Liu

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

Optimization and Control · Mathematics 2019-10-18 Romeo Ortega , Vladislav Gromov , Emmanuel Nuño , Anton Pyrkin , Jose Guadalupe Romero

We study the problem of robust time series analysis under the standard auto-regressive (AR) time series model in the presence of arbitrary outliers. We devise an efficient hard thresholding based algorithm which can obtain a consistent…

Machine Learning · Computer Science 2016-07-04 Kush Bhatia , Prateek Jain , Parameswaran Kamalaruban , Purushottam Kar

This research focuses on the estimation of a non-parametric regression function designed for data with simultaneous time and space dependencies. In such a context, we study the Trend Filtering, a nonparametric estimator introduced by…

Methodology · Statistics 2023-09-14 Carlos Misael Madrid Padilla , Oscar Hernan Madrid Padilla , Daren Wang

We consider a two-level discrete-time control framework with real-time constraints where a central controller issues setpoints to be implemented by local controllers. The local controllers implement the setpoints with some approximation and…

Optimization and Control · Mathematics 2016-12-22 Andrey Bernstein , Niek J. Bouman , Jean-Yves Le Boudec

This article develops a general detection theory for speech analysis based on time-varying autoregressive models, which themselves generalize the classical linear predictive speech analysis framework. This theory leads to a computationally…

Applications · Statistics 2011-08-25 Daniel Rudoy , Thomas F. Quatieri , Patrick J. Wolfe

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…

Statistics Theory · Mathematics 2024-03-12 Sara Mazzonetto , Paolo Pigato

This paper investigates the optimality analysis of the recursive least-squares (RLS) algorithm for autoregressive systems with exogenous inputs (ARX systems). A key challenge in analyzing is managing the potential unboundedness of the…

Optimization and Control · Mathematics 2025-05-27 Xingrui Liu , Jieming Ke , Yanlong Zhao

Exponentially stable extended adaptive observer is proposed for a class of linear time-invariant systems with unknown parameters and overparameterization. It allows one to reconstruct unmeasured states and bounded external disturbance…

Systems and Control · Electrical Eng. & Systems 2023-01-19 Anton Glushchenko , Konstantin Lastochkin

This paper examines the asymptotic inference for AR(1) models with a possible structural break in the AR parameter $\beta $ near the unity at an unknown time $k_{0}$. Consider the model $y_{t}=\beta_{1}y_{t-1}I\{t\leq k_{0}\}+\beta…

Statistics Theory · Mathematics 2013-06-07 Pang Tianxiao , Zhang Danna , Chong Terence Tai-Leung

This work presents a new sufficient condition for synthesizing nonlinear controllers that yield bounded closed-loop tracking error transients despite the presence of unmatched uncertainties that are concurrently being learned online. The…

Systems and Control · Electrical Eng. & Systems 2023-10-23 Samuel G. Gessow , Brett T. Lopez

Empirical risk minimization is a standard principle for choosing algorithms in learning theory. In this paper we study the properties of empirical risk minimization for time series. The analysis is carried out in a general framework that…

Machine Learning · Statistics 2021-08-12 Christian Brownlees , Jordi Llorens-Terrazas

This paper considers the problem of matrix-variate logistic regression. It derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by obtaining a lower bound on the minimax…

Machine Learning · Computer Science 2022-05-10 Batoul Taki , Mohsen Ghassemi , Anand D. Sarwate , Waheed U. Bajwa

Nonlinear systems of affine control inputs overarch many sensor fusion instances. Analyzing whether a state variable in such a nonlinear system can be estimated (i.e., observability) informs better estimator design. Among the research on…

Systems and Control · Electrical Eng. & Systems 2022-07-19 Jianzhu Huai , Yukai Lin , Yujia Zhang

In a decision-theoretic framework, the minimax lower bound provides the worst-case performance of estimators relative to a given class of statistical models. For parametric and semiparametric models, the H\'{a}jek--Le Cam local asymptotic…

Statistics Theory · Mathematics 2024-10-22 Kenta Takatsu , Arun Kumar Kuchibhotla

This paper provides some extended results on estimating parameter matrix of several regression models when the covariate or response possesses weaker moment condition. We study the $M$-estimator of Fan et al. (Ann Stat 49(3):1239--1266,…

Statistics Theory · Mathematics 2022-09-08 Kangqiang Li , Songqiao Tang , Lixin Zhang

Inspired by classical sensitivity results for nonlinear optimization, we derive and discuss new quantitative bounds to characterize the solution map and dual variables of a parametrized nonlinear program. In particular, we derive explicit…

Optimization and Control · Mathematics 2020-06-19 Irina Subotić , Adrian Hauswirth , Florian Dörfler

A Vector Auto-Regressive (VAR) model is commonly used to model multivariate time series, and there are many penalized methods to handle high dimensionality. However in terms of spatio-temporal data, most methods do not take the spatial and…

Methodology · Statistics 2020-12-21 Zhenzhong Wang , Abolfazl Safikhani , Zhengyuan Zhu , David S. Matteson