Non-Asymptotic Confidence Regions for the Least-Squares Estimate

Csáji, Balázs Csanád; Campi, Marco C.; Weyer, Erik

doi:10.3182/20120711-3-be-2027.00417

Cited by 19 publications

(44 citation statements)

References 5 publications

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“…In Campi and Weyer [2005], Dalai et al [2007], Csáji et al [2012], two new approaches named LSCR and SPS are described for the exact characterization of parameter uncertainty in non-asymptotic conditions. Their most striking feature is that they avoid a large number of the usual assumptions about the noise corrupting the data.…”

Section: Characterizing Parameter Uncertainty With the Lscr Approachmentioning

confidence: 99%

Guaranteed characterization of exact non-asymptotic confidence regions in nonlinear parameter estimation

Kieffer¹,

Walter²

2013

IFAC Proceedings Volumes

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Abstract:Recently, a new family of methods has been proposed for characterizing accuracy in nonlinear parameter estimation by Campi et al.. These methods make it possible to obtain exact, nonasymptotic confidence regions for the parameter estimates under relatively mild assumptions on the noise distribution, namely that the noise samples are independently and symmetrically distributed. The numerical characterization of an exact confidence region with this new approach is far from being trivial, however. The aim of this paper is to show how interval analysis, which has been used for a guaranteed characterization of confidence regions for the parameter vector in other contexts, can contribute.

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Section: Characterizing Parameter Uncertainty With the Lscr Approachmentioning

confidence: 99%

Guaranteed characterization of exact non-asymptotic confidence regions in nonlinear parameter estimation

Kieffer¹,

Walter²

2013

IFAC Proceedings Volumes

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“…This limitation makes the new methods LSCR and SPS proposed by Campi and coworkers particularly interesting [1], [3], [4].…”

Section: Spsmentioning

confidence: 99%

“…In [3], it has been shown that p * belongs to Σ q with exact probability 1 − q/m. Σ q may be defined more formally as…”

Section: Spsmentioning

confidence: 99%

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Guaranteed characterization of exact confidence regions for FIR models under mild assumptions on the noise via interval analysis

Kieffer¹,

Walter²

2013

52nd IEEE Conference on Decision and Control

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Abstract-SPS is one of the two methods proposed recently by Campi et al. to obtain exact, non-asymptotic confidence regions for parameter estimates under mild assumptions on the noise distribution. It does not require the measurement noise to be Gaussian (or to have any other known distribution for that matter). The numerical characterization of the resulting confidence regions is far from trivial, however, and has only be carried out so far on very low-dimensional problems via methods that could not guarantee their results and could not be extended to large-scale problems because of their intrinsic complexity. The aim of the present paper is to show how interval analysis can contribute to a guaranteed characterization of exact confidence regions in large-scale problems. The application considered is the estimation of the parameters of finite-impulseresponse (FIR) models. The structure of the problem makes it possible to define a very efficient specific contractor, allowing the treatement of models with a large number of parameters, as is the rule for FIR models, and thus escaping the curse of dimensionality that often plagues interval methods.

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“…When a vector p of parameters of some approximate mathematical model is estimated from a noisy data vector y, this is usually via the minimization of some cost function J (p), for instance J (p) = y − y m (p) 2 2 , where y m (p) is the vector of model outputs, assumed here to be a deterministic function of p and · 2 is a (possibly weighted) ℓ 2 norm. Then…”

Section: Introductionmentioning

confidence: 99%

Guaranteed characterization of exact non-asymptotic confidence regions as defined by LSCR and SPS

Kieffer

Walter

2014

Automatica

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In parameter estimation, it is often desirable to supplement the estimates with an assessment of their quality. A new family of methods proposed by Campi et al. for this purpose is particularly attractive, as it makes it possible to obtain exact, nonasymptotic confidence regions under relatively mild assumptions on the noise distribution. A bottleneck of this approach, however, is the numerical characterization of these confidence regions. So far, it has been carried out by gridding, which provides no guarantee as to its results and is only applicable to low dimensional spaces. The aim of this paper is to show how interval analysis can contribute to removing this bottleneck.

show abstract

Non-Asymptotic Confidence Regions for the Least-Squares Estimate

Cited by 19 publications

References 5 publications

Guaranteed characterization of exact non-asymptotic confidence regions in nonlinear parameter estimation

Guaranteed characterization of exact non-asymptotic confidence regions in nonlinear parameter estimation

Guaranteed characterization of exact confidence regions for FIR models under mild assumptions on the noise via interval analysis

Guaranteed characterization of exact non-asymptotic confidence regions as defined by LSCR and SPS

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