Parameter Estimation and Hypothesis Testing in Linear Models

Koch, Karl‐Rudolf

doi:10.1007/978-3-662-03976-2

Cited by 819 publications

(103 citation statements)

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“…We formed the design matrix A given in Eq. (18), and the unknown parameters are From the above results, the simple derived formula based on the robust approach produces better solutions for estimating baseline distances. In the previous studies, the conventional least square approach was only used for estimating calibration parameters of EDM [2,7,8].…”

Section: Real Baselinesmentioning

confidence: 90%

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A Novel Robust Scaling for EDM Calibration Baselines using Monte Carlo Study

Erenoǧlu

2018

Teh. vjesn.

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Abstract:The terrestrial measurements using Electronic Distance Measurement (EDM) have been widely done for different applications such as deformation monitoring and establishing geodetic networks. The calibration of the EDMs reflects the quality of the estimated parameters. In geodesy, least squares principle is mainly used for estimating parameters. The least square estimation is adversely affected by the systematic and non-systematic errors resulting in bias for the estimated parameters. In this study, to compare efficacy of different robust methods, the Monte Carlo simulation is applied to the EDM calibration as well as real experiments. The parameters without errors are obtained as a result of the used methodology. The methods given in this study are basically based on iteratively reweighted least squares and can be used for both parameter estimation and outlier diagnostics. This is of particular importance for calibrations of electromagnetic distance measurements using the Monte Carlo simulation and the measured test baselines. The results showed that one of the advantages of the used methodology is the improvement of the reliability of the estimated calibration parameters.

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Section: Real Baselinesmentioning

confidence: 90%

“…Iteratively reweighted LS estimation can be used to solve non-linear normal equation system of the M-estimation [18]. The M-estimation of Huber, the Mestimation of Hampel, the M-estimation of Andrews, the Danish method, the L 1 -norm and the IGGIII scheme were used [9,10,[19][20][21][22][23].…”

Section: Outlier Conceptmentioning

confidence: 99%

A Novel Robust Scaling for EDM Calibration Baselines using Monte Carlo Study

Erenoǧlu

2018

Teh. vjesn.

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“…Finally, each VTEC i value is compared with the threshold value of a certain (k) times mad. k is here taken as 3 [27,31]. If the absolute value of VTECi is bigger than the threshold, it is flagged as a discordant value, and then removed from the data set.…”

Section: A New Methods For Regional Vtec Mappingmentioning

confidence: 99%

“…The outlying data should be therefore excluded from the data set. Most of them are based on the LSE method, and so they do not always produce reliable solutions [27,28,29], although there exist some methods for analysing the quality of the TEC estimation, see [30]. For removing the effect of outlying data, a novel approach which reflects the quality of the data, can be utilized [31].…”

Section: Introductionmentioning

confidence: 99%

A new approach to outlying data in estimation of vertical total electron content

Erenoǧlu

2015

Teh. vjesn.

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Original scientific paper For all scientific studies, for processing analytical data the subject of outliers is of critical importance. The accuracy of Total Electron Content (TEC) models obtained from ground based Global Positioning Systems (GPS) data is strongly affected by some factors such as satellite geometry, cut-off angle, ionospheric shell height, quantity of GPS data etc. Probable outliers within the observables have a significant effect on the quality of the estimated TEC modelling. These should be removed from the TEC time series in order to get more reliable results for further process. Although some analytical methods have been developed for the code-outliers, phase-slips and ionosphere disturbances, significant reduction in the number of measurement could adversely affect the quality of the generated TEC values using geometry-free combinations of those. In this study, we proposed a novel approach for outlier detection to be used at geometry-free combinations in estimation of vertical TEC without reducing the number of code observables. Here the GPS data obtained from 22 permanent stations are used to estimate the VTEC on May 14-15, 2005. The research results from the detailed processing clearly show the efficiency of the method. Our research shows that the proposed approach appears to be a fast, effective and objective method to detect outlying effects which cause improper modelling. Moreover the resulting VTEC maps from the new approach differ reliably with respect to the data including outlying observables. Consequently, the proposed method could provide an alternative to outlier rejection in estimation of VTEC, in which outlying observations are retained in geometry-free combinations. Keywords: discordant data; GPS; median; outlier; total electron content Novi pristup vanjskim (outlying) podacima u procjeni vertikalnog ukupnog sadržaja elektronaIzvorni znanstveni članak U svim vrstama znanstvenih studija, za obradu analitičkih podataka pitanje outliera je od bitne važnosti. Na točnost Total Electron Content (TEC) modela koja se postiže na temelju podataka Sustava za Globalno Pozicioniranje (GPS) sa zemlje uvelike djeluju čimbenici kao što su geometrija satelita, kut prekida, visina ionosferske ljuske, količina GPS podataka i sl. Vjerojatni outlieri među promatranima imaju značajan učinak na kvalitetu procijenjenog TEC modeliranja. Njih je potrebno ukloniti iz TEC vremenskih serija kako bi se dobili pouzdaniji rezultati za daljnji postupak. Iako su neke analitičke metode razvijene za code-outliers, phase-slips i poremećaje u ionosferi, značajno smanjenje broja mjerenja negativno bi moglo utjecati na kvalitetu nastalih TEC vrijednosti primjenom njihovih kombinacija bez geometrije. U ovom istraživanju, predložili smo novi pristup za otkrivanje outliera koji će se koristiti u kombinacijama bez geometrije u procjeni vertikalnog TEC-a bez smanjenja broja promatrača koda. Ovdje se GPS podaci dobiveni iz 22 stalnih postaja koriste za procjenu VTEC-a na dan 14-15 svibnja 2005. Rezultati istraživanja dob...

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“…The point in reference block whose contribution to the quadric form R is maximum is considered responsible for the rejection of H 0 . This procedure is carried out until the null hypothesis is satisfied (Niemeier, 1977;Koch, 1999;Caspary, 1987;Denli and Deniz, 2003;Yalçınkaya, 2003). Tables 1 and 2 were calculated according to Koch (1999).…”

Section: Static Analysismentioning

confidence: 99%

Modelling the relationship between water level and vertical displacements on the Yamula Dam, Turkey

Bayrak

2007

Nat. Hazards Earth Syst. Sci.

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Abstract. Monitoring deformation pattern of dams is often one of the most effective ways to understand their safety status. The main objective of the study is to find the extent to which rising reservoir level affects the mechanism of deformation of The Yamula Dam under certain change in the reservoir level conditions during to the first filling period. Three different deformation analysis techniques, namely static, kinematic and dynamic, were used to analyze four geodetic monitoring records consisting of vertical displacements of nine object points established on the Dam and six reference points surrounding of it, to see whether the rising reservoir level have a role in the vertical deformations during the first filling period. The largest vertical displacements were in the middle of the dam. There is an apparent linear relationship between the dam subsidence and the reservoir level. A dynamic deformation model was developed to model this situation. The model infers a causative relationship between the reservoir level and the dam deformations. The analysis of the results determines the degree of the correlation between the change in the reservoir level and the observed structural deformation of the dam.

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Parameter Estimation and Hypothesis Testing in Linear Models

Cited by 819 publications

References 0 publications

A Novel Robust Scaling for EDM Calibration Baselines using Monte Carlo Study

A Novel Robust Scaling for EDM Calibration Baselines using Monte Carlo Study

A new approach to outlying data in estimation of vertical total electron content

Modelling the relationship between water level and vertical displacements on the Yamula Dam, Turkey

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