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

Kieffer, Michel; Walter, Éric

doi:10.1016/j.automatica.2013.11.010

Cited by 26 publications

(31 citation statements)

References 11 publications

(20 reference statements)

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“…Illustrations have been provided for two models with outputs nonlinear in their parameters. Applications to the characterization of confidence regions defined by SPS may be found in Kieffer and Walter [2012].…”

Section: Discussionmentioning

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: Discussionmentioning

confidence: 99%

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

Kieffer¹,

Walter²

2013

IFAC Proceedings Volumes

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“…For SPS, computationally feasible approximations techniques have been studied that rely on interval analysis, e.g. (Kieffer and Walter, 2013), or on semidefinite programming (SDP), (Csáji et al, 2015). We focus here on the latter option, which allows us to compute outer ellipsoidal approximations of SPS regions.…”

Section: Computational Feasibility Of the Ud-sps Algorithmmentioning

confidence: 99%

Undermodelling Detection with Sign-Perturbed Sums

et al. 2017

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Sign-Perturbed Sums (SPS) is a finite sample system identification method that can build exact confidence regions for the unknown parameters of linear systems under mild statistical assumptions. Theoretical studies of the SPS method have assumed so far that the order of the system model is known to the user. In this paper we discuss the implications of this assumption for the applicability of the SPS method, and we propose an extension that, under mild assumptions, i) still delivers guaranteed confidence regions when the model order is correct, and ii) it is guaranteed to detect, in the long run, if the model order is wrong.

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“…An alternative approach based on interval analysis has been proposed in (16). Its main property is to yield inner and outer approximations of P e,q,m consisting of unions of non-overlapping boxes.…”

Section: Characterizing Confidence Regionsmentioning

confidence: 99%

“…Nevertheless, the confidence region as defined by LSCR may be non-convex or even may consist of several disconnected components. As shown in (16), using tools from interval analysis (12), one is able to obtain inner and outer approximations of the confidence regions as defined by LSCR using subpavings, i.e., set of non-overlapping interval vectors.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed confidence region characterization for source localization using RSS measurements

2018

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This paper considers source localization in a Wireless Sensor Network (WSN) from Received Signal Strength (RSS) measurements. Its aim is to characterize confidence regions (CR) of the search space to which the source parameters (location, reference power, path loss exponent) are guaranteed to belong with a pre-specified probability level. The Leave-out Signdominant Correlation Regions (LSCR) method is adapted to this source localization context. LSCR defines CR considering very mild assumptions on the measurement noise corrupting the RSS readings. The confidence level may be arbitrarily chosen and the LSCR approach is valid even when very few measurements are available (non-asymptotic regime). The CR, as defined by LSCR may be non-convex or even non-connected sets. Their characterization is performed via interval analysis, which provides inner and outer approximations of CR.The CR obtained via LSCR are compared to set estimates obtained using (robust) bounded-error estimation techniques, as well as to more classical confidence ellipsoids derived from Cramér-Rao lower bounds.

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

Cited by 26 publications

References 11 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

Undermodelling Detection with Sign-Perturbed Sums

Guaranteed confidence region characterization for source localization using RSS measurements

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