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We develop a class of exponential bounds for the probability that a martingale sequence crosses a time-dependent linear threshold. Our key insight is that it is both natural and fruitful to formulate exponential concentration inequalities…

Probability · Mathematics 2025-12-18 Steven R. Howard , Aaditya Ramdas , Jon McAuliffe , Jasjeet Sekhon

The celebrated Nadaraya-Watson kernel estimator is among the most studied method for nonparametric regression. A classical result is that its rate of convergence depends on the number of covariates and deteriorates quickly as the dimension…

Statistics Theory · Mathematics 2017-11-28 Daniel Conn , Gang Li

We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the…

Probability · Mathematics 2007-05-23 Mohamed El Machkouri , Lahcen Ouchti

This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…

Statistics Theory · Mathematics 2019-09-24 Evgeny Pchelintsev , Serguei Pergamenshchikov

We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…

Statistics Theory · Mathematics 2007-06-13 Mohamed El Machkouri

In this paper, we derive the moderate deviation principle for stationary sequences of bounded random variables with values in a Hilbert space. The conditions obtained are expressed in terms of martingale-type conditions. The main tools are…

Probability · Mathematics 2009-01-21 Sophie Dede

We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…

Statistics Theory · Mathematics 2014-01-07 Xiaohui Chen , Mengyu Xu , Wei Biao Wu

In this paper, we consider the time-inhomogeneous nonlinear time series regression for a general class of locally stationary time series. On one hand, we propose sieve nonparametric estimators for the time-varying regression functions which…

Statistics Theory · Mathematics 2021-12-17 Xiucai Ding , Zhou Zhou

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…

Statistics Theory · Mathematics 2007-06-13 Eric Moulines , Pierre Priouret , François Roueff

We propose a modified weighted Nadaraya-Watson estimator for the conditional distribution of a time series with heavy tails. We establish the asymptotic normality of the proposed estimator. Simulation study is carried out to assess the…

Statistics Theory · Mathematics 2024-07-23 Deemat C Mathew , Hareesh G , Sudheesh , K Kattumannil

Compared to the nominal scale, the ordinal scale for a categorical outcome variable has the property of making a monotonicity assumption for the covariate effects meaningful. This assumption is encoded in the commonly used proportional odds…

Methodology · Statistics 2023-10-04 Olli Saarela , Christian Rohrbeck , Elja Arjas

The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…

Statistics Theory · Mathematics 2010-10-20 Victor Konev , Serguei Pergamenchtchikov

The general regularisation scheme, a versatile approach for nonparametric estimation, has been successfully applied to regression, density ratio, and score estimation. In this paper, we introduce a unified framework encompassing these…

Statistics Theory · Mathematics 2026-05-12 Gilles Germain

Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of $k$ arguments is assumed to be continuous with…

Statistics Theory · Mathematics 2023-07-04 Yu. Yu. Linke , I. S. Borisov , P. S. Ruzankin

In this paper, we give rates of convergence, for minimal distances and for the uniform distance, between the law of partial sums of martingale differences and thelimiting Gaussian distribution. More precisely, denoting by $P_{X}$ the law of…

Probability · Mathematics 2021-01-19 Jérôme Dedecker , Florence Merlevède , Emmanuel Rio

This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or…

Systems and Control · Electrical Eng. & Systems 2025-03-25 Jieming Ke , Ying Wang , Yanlong Zhao , Ji-Feng Zhang

We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…

Probability · Mathematics 2017-03-24 Hanchao Wang , Zhengyan Lin , Zhonggen Su

Considering a class of gradient-based multi-agent learning algorithms in non-cooperative settings, we provide local convergence guarantees to a neighborhood of a stable local Nash equilibrium. In particular, we consider continuous games…

Optimization and Control · Mathematics 2024-09-23 Benjamin Chasnov , Lillian J. Ratliff , Eric Mazumdar , Samuel A. Burden

A new approach is developed for evaluating the convergence rate for nonlinear Markov chains (MC) based on the recently developed spectral radius technique of markovian coupling for linear MC and the idea of small nonlinear perturbations of…

Probability · Mathematics 2025-03-27 Alexander Shchegolev , Alexander Veretennikov

Estimating the impact of continuous treatment variables (e.g., dosage amount) on binary outcomes presents significant challenges in modeling and estimation because many existing approaches make strong assumptions that do not hold for…

Methodology · Statistics 2025-05-08 Muyan Jiang , Yunkai Zhang , Anil Aswani