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Hu, Xiaoyi; Huang, C.; Liao, Xi

doi:10.1023/a:1013204418865

Cited by 4 publications

(2 citation statements)

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“…Considering contemporary observations, we should expect a wider range of the kurtosis values. For example, in the case of the observations from Satellite Laser Ranging, the kurtosis ranging β 2 = 2.69 ÷ 9.46 (Hu et al, 2001), and for GPS observations β 2 = 2.79 ÷ 3.29 ( Luo et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

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MP estimation applied to platykurtic sets of geodetic observations

Wiśniewski¹

2017

Geodesy and Cartography

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M P estimation is a method which concerns estimating of the location parameters when the probabilistic models of observations differ from the normal distributions in the kurtosis or asymmetry. The system of Pearson's distributions is the probabilistic basis for the method. So far, such a method was applied and analyzed mostly for leptokurtic or mesokurtic distributions (Pearson's distributions of types IV or VII), which predominate practical cases. The analyses of geodetic or astronomical observations show that we may also deal with sets which have moderate asymmetry or small negative excess kurtosis. Asymmetry might result from the infl uence of many small systematic errors, which were not eliminated during preprocessing of data. The excess kurtosis can be related with bigger or smaller (in relations to the Hagen hypothesis) frequency of occurrence of the elementary errors which are close to zero. Considering that fact, this paper focuses on the estimation with application of the Pearson platykurtic distributions of types I or II. The paper presents the solution of the corresponding optimization problem and its basic properties. Although platykurtic distributions are rare in practice, it was an interesting issue to fi nd out what results can be provided by M P estimation in the case of such observation distributions. The numerical tests which are presented in the paper are rather limited; however, they allow us to draw some general conclusions.

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Section: Introductionmentioning

confidence: 99%

“…Actually, such distributions predominate in astronomical and geodetic observations; however, they do not cover all the possible cases (e.g. Hu et al, 2001;Luo et al, 2011). Thus, there is a need for consideration M P estimation for distributions which excess kurtosis is negative.…”

Section: Introductionmentioning

confidence: 99%

MP estimation applied to platykurtic sets of geodetic observations

Wiśniewski¹

2017

Geodesy and Cartography

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M-estimation with probabilistic models of geodetic observations

Wiśniewski

2014

J Geod

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The paper concerns M-estimation with probabilistic models of geodetic observations that is called M P estimation. The special attention is paid to M P estimation that includes the asymmetry and the excess kurtosis, which are basic anomalies of empiric distributions of errors of geodetic or astrometric observations (in comparison to the Gaussian errors). It is assumed that the influence function of M P estimation is equal to the differential equation that defines the system of the Pearson distributions. The central moments μ k , k = 2, 3, 4, are the parameters of that system and thus, they are also the parameters of the chosen influence function. The M P estimation that includes the Pearson type IV and VII distributions (M PD(l) method) is analyzed in great detail from a theoretical point of view as well as by applying numerical tests. The chosen distributions are leptokurtic with asymmetry which refers to the general characteristic of empirical distributions. Considering M-estimation with probabilistic models, the Gram-Charlier series are also applied to approximate the models in question (M G−C method). The paper shows that M P estimation with the application of probabilistic models belongs to the class of robust estimations; M PD(l) method is especially effective in that case. It is suggested that even in the absence of significant anomalies the method in question should be regarded as robust against gross errors while its robustness is controlled by the pseudo-kurtosis.

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Leptokurtosis of Error Distribution and its Influence on Estimation Accuracy. The Case of Three Estimates Applied in Adjustment of Geodetic Measurements

Duchnowski¹,

Wyszkowska²

2017

2017 Baltic Geodetic Congress (BGC Geomatics)

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Cited by 4 publications

References 10 publications

MP estimation applied to platykurtic sets of geodetic observations

MP estimation applied to platykurtic sets of geodetic observations

M-estimation with probabilistic models of geodetic observations

Leptokurtosis of Error Distribution and its Influence on Estimation Accuracy. The Case of Three Estimates Applied in Adjustment of Geodetic Measurements

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