Linear Models

Rao, C. Radhakrishna; Toutenburg, Helge

doi:10.1007/978-1-4899-0024-1

Cited by 218 publications

(61 citation statements)

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“…(9) and (10) are known, and the nonlinear functions F (x) and G(x) can be obtained by leastsquares fitting using low-order polynomials (Yan et al, 2009;Komhyr et al, 1983Komhyr et al, , 1989Bjorck, 1996;Rao et al, 1999;Derek, 1968;Marcel et al, 1990). Therefore, gases i and j have measurement errors of γ i and γ j because of the variations of calibration curves and interference coefficients.…”

Section: Y W Sun Et Al: Stack Emission Monitoring 1995mentioning

confidence: 99%

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Stack emission monitoring using non-dispersive infrared spectroscopy with an optimized nonlinear absorption cross interference correction algorithm

et al. 2013

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In this paper, we present an optimized analysis algorithm for non-dispersive infrared (NDIR) to in situ monitor stack emissions. The proposed algorithm simultaneously compensates for nonlinear absorption and cross interference among different gases. We present a mathematical derivation for the measurement error caused by variations in interference coefficients when nonlinear absorption occurs. The proposed algorithm is derived from a classical one and uses interference functions to quantify cross interference. The interference functions vary proportionally with the nonlinear absorption. Thus, interference coefficients among different gases can be modeled by the interference functions whether gases are characterized by linear or nonlinear absorption. In this study, the simultaneous analysis of two components (CO₂ and CO) serves as an example for the validation of the proposed algorithm. The interference functions in this case can be obtained by least-squares fitting with third-order polynomials. Experiments show that the results of cross interference correction are improved significantly by utilizing the fitted interference functions when nonlinear absorptions occur. The dynamic measurement ranges of CO₂ and CO are improved by about a factor of 1.8 and 3.5, respectively. A commercial analyzer with high accuracy was used to validate the CO and CO₂ measurements derived from the NDIR analyzer prototype in which the new algorithm was embedded. The comparison of the two analyzers show that the prototype works well both within the linear and nonlinear ranges

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Section: Y W Sun Et Al: Stack Emission Monitoring 1995mentioning

confidence: 99%

“…γ j = 0 absorption. Bjorck, 1996;Rao et al, 1999;Derek, 1968;Marcel et al, 1990), which is similar to the acquisition method for calibration curves. Details of the procedure are as follows.…”

Section: An Optimized Algorithmmentioning

confidence: 99%

Stack emission monitoring using non-dispersive infrared spectroscopy with an optimized nonlinear absorption cross interference correction algorithm

et al. 2013

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“…Under this assumptions it is well known (Rao et al (1997)) that the LS identification of the parameter θ is given by:…”

Section: Least-squares Estimationmentioning

confidence: 99%

Channel Model Identification in Wireless Sensor Networks Using a Fully Distributed Quantized Consensus Algorithm

Cenedese

Zanella

2014

IFAC Proceedings Volumes

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In this paper, we consider the problem of designing a distributed strategy to estimate the channel parameters for a generic Wireless Sensor-Actor Network (WSAN). To this aim, we present a distributed least-square algorithm that complies with the constraint of transmitting only integer data through the wireless communication, which often characterizes WSAN embedded architectures. In this respect, we propose a quantized consensus strategy that mitigates the effects of the rounding operations applied to the wireless exchanged floating data. Moreover, the approach is based on a symmetric random gossip strategy, making it suitable for the actual deployment in multiagent networks. Finally, the effectiveness of the proposed algorithm and of its implementation as an open-source application is assessed and the employment of the procedure is illustrated through the application to radio-frequency localization experiments in a real world testbed.

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“…A n alternative solution is to plug in imputed values for missing observations and then to carry out the regression analysis. Such imputed values can be obtained in several ways see, e.g., Little and Rubin (1987) for basic considerations and Little (1992) for a detailed discussion of missing X-values in regression, and Rao and Toutenburg (1995) for a detailed account of MDE-superiority i n vestigations for imputation methods. When these imputed values are non-stochastic, the application of the least squares procedure for the estimation of regression coe cients generally yields biased and inconsistent estimators see, e.g., Toutenburg, Heumann, Fieger and Park (1995), who have examined the e ciency properties of such procedures with respect to the procedure that uses only the complete observations and provides unbiased estimators of regression coe cients.…”

Section: Introductionmentioning

confidence: 99%

“…e.g. Rao and Toutenburg, 1995, for the derivation of the weighted mixed regression estimator). As a generalization of the MFOR estimator^ from (2.10) we i n troduce a weight w, 0 w 1 and incorporate it in^ in the following manner^ wMFOR = ( X 0 c X c + w 2X0 X ) ;1 (X 0 c y c + w 2X0 y ) (2.11) This estimator is called the weighted MFOR estimator (wMFOR).…”

Section: Introductionmentioning

confidence: 99%

Weighted modified first order regression procedures for estimation in linear models with missingX-observations

Toutenburg¹,

Fieger²,

Srivastava

1999

Statistical Papers

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This paper considers the estimation of coe cients in a linear regression model with missing observations in the independent v ariables and introduces a modi cation of the standard rst order regression method for imputation of missing values. The modi cation provides stochastic values for imputation and, as an extension, makes use of the principle of weighted mixed regression. The proposed procedures are compared with two popular procedures|one which utilizes only the complete observations and the other which employs the standard rst order regression imputation method for missing values.A simulation experiment t o e v aluate the gain in e ciency and to examine interesting issues like the impact of varying degree of multicollinearity in explanatory variables is proceeded. Some work on the case of discrete regressor variables is in progress and will be reported in a future article to follow.

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Linear Models

Cited by 218 publications

References 0 publications

Stack emission monitoring using non-dispersive infrared spectroscopy with an optimized nonlinear absorption cross interference correction algorithm

Stack emission monitoring using non-dispersive infrared spectroscopy with an optimized nonlinear absorption cross interference correction algorithm

Channel Model Identification in Wireless Sensor Networks Using a Fully Distributed Quantized Consensus Algorithm

Weighted modified first order regression procedures for estimation in linear models with missingX-observations

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