
Finite sample deviation and variance bounds for first order autoregressive processes
In this paper, we study finitesample properties of the least squares es...
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Sharp finitesample large deviation bounds for independent variables
We show an extension of Sanov's theorem in large deviations theory, cont...
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Finite impulse response models: A nonasymptotic analysis of the least squares estimator
We consider a finite impulse response system with centered independent s...
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Bump detection in the presence of dependency: Does it ease or does it load?
We provide the asymptotic minimax detection boundary for a bump, i.e. an...
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Risk Bounds for Infinitely Divisible Distribution
In this paper, we study the risk bounds for samples independently drawn ...
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Moderate deviations in a class of stable but nearly unstable processes
We consider a stable but nearly unstable autoregressive process of any o...
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Finitetime Identification of Stable Linear Systems: Optimality of the LeastSquares Estimator
We provide a new finitetime analysis of the estimation error of stable ...
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A FiniteSample Deviation Bound for Stable Autoregressive Processes
In this paper, we study nonasymptotic deviation bounds of the least squares estimator in Gaussian AR(n) processes. By relying on martingale concentration inequalities and a tailbound for χ^2 distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, we present a problemdependent finitetime bound on the deviation probability of any fixed linear combination of the estimated parameters of the AR(n) process. We discuss extensions and limitations of our approach.
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