On upper bounds for the variance of functions of random variables

Cacoullos, T.; Papathanasiou, V.

doi:10.1016/0167-7152(85)90014-8

Cited by 61 publications

(28 citation statements)

References 3 publications

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“…But if one were to use a nonlinear activation function such as the tangent hyperbolic sigmoid function, f (x) = 2 1+e −2x − 1, then the variance becomes quite difficult to determine analytically. However, from [5], we have the following upper bound on the variance of the function g(X) of a random variable X, if X ∼ N (µ, σ 2 ):…”

Section: Regularization Using Error Covariance Matricesmentioning

confidence: 99%

“…The communication delay also reduces the chance that a message is successfully received by the fusion center by a certain deadline. Therefore, with incomplete sensor data, the fusion center could use predicted estimates it derives for the individual sensors, and once these predicted values are obtained 5 , the inputs to the ANNs are complete. Training data may contain such predicted estimates too.…”

Section: B Fusion Performance Without Sensor Biasesmentioning

confidence: 99%

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Estimation and Fusion for Tracking Over Long-Haul Links Using Artificial Neural Networks

Liu

Brigham

Rao

2017

IEEE Trans. on Signal and Inf. Process. over Networks

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Nageswara S. V. (2017) 'Estimation and fusion for tracking over long-haul links using articial neural networks.', IEEE transactions on signal and information processing over networks., 3 (4). pp. 760-770. Further information on publisher's website: Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract-In a long-haul sensor network, sensors are remotely deployed over a large geographical area to perform certain tasks, such as tracking and/or monitoring of one or more dynamic targets. A remote fusion center fuses the information provided by these sensors so that a final estimate of certain target characteristics -such as the position -is expected to possess much improved quality. In this work, we pursue learning-based approaches for estimation and fusion of target states in longhaul sensor networks. In particular, we consider learning based on various implementations of artificial neural networks (ANNs). The joint effect of (i) imperfect communication condition, namely, link-level loss and delay, and (ii) computation constraints, in the form of low-quality sensor estimates, on ANN-based estimation and fusion, is investigated by means of analytical and simulation studies.Index Terms-Long-haul sensor networks, state estimate fusion, artificial neural networks, estimation bias, error regularization, root-mean-square-error (RMSE) performance, reporting deadline.

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Section: Regularization Using Error Covariance Matricesmentioning

confidence: 99%

Section: B Fusion Performance Without Sensor Biasesmentioning

confidence: 99%

Estimation and Fusion for Tracking Over Long-Haul Links Using Artificial Neural Networks

Liu

Brigham

Rao

2017

IEEE Trans. on Signal and Inf. Process. over Networks

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“…The following Lemma summarizes and unifies these bounds in terms of the r.v. X * ; in effect, (3.1) is a Chernoff-type, [8], upper bound; (3.2) is a Cacoullos-type, [14], [15], lower bound as obtained in [1] and [3], in terms of a function w (see also (3.4) below). …”

Section: Application To Variance Boundsmentioning

confidence: 99%

“…This example hinges on the fact that S(X) fails to be an interval. If, however, S(X) is a (finite or infinite) interval, the known upper and lower bounds for the variance of g(X) take the form (see [3], [4])…”

Section: Application To Variance Boundsmentioning

confidence: 99%

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Unified Variance Bounds and a Stein-Type Identity

Papadatos¹,

Papathanasiou²

2000

Probability and Statistical Models With Applications

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Let X be an absolutely continuous (a.c.) random variable (r.v.) with finite variance σ 2 . Then, there exists a new r.v. X * (which can be viewed as a transform on X) with a unimodal density, satisfying the extended Stein-type covariance identityfor any a.c. function g with derivative g , provided that IE|g (X * )| < ∞. Properties of X * are discussed and, also, the corresponding unified upper and lower bounds for the variance of g(X) are derived.

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Inequalities,Cacoullos‐Type

Cacoullos¹,

Papathanasiou²

2004

Encyclopedia of Statistical Sciences

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On upper bounds for the variance of functions of random variables

Cited by 61 publications

References 3 publications

Estimation and Fusion for Tracking Over Long-Haul Links Using Artificial Neural Networks

Estimation and Fusion for Tracking Over Long-Haul Links Using Artificial Neural Networks

Unified Variance Bounds and a Stein-Type Identity

Inequalities,Cacoullos‐Type

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