Improved critical values for extreme normalized and studentized residuals in Gauss–Markov models

Lehmann, Rüdiger

doi:10.1007/s00190-012-0569-0

Cited by 70 publications

(79 citation statements)

References 8 publications

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“…If on the contrary this level is chosen too high then we get too small critical values and it is likely that good observations are eliminated. Lehmann (2012) shows how to strike a balance between these impairments of parameter estimation by using MCS methods. The γ0 represents the efficiency level of the DS to identify correctly an outlying observation.…”

Section: Methods Proposal To Design Geodetic Networkmentioning

confidence: 99%

“…The basic idea is to approximate probability distributions by frequency distributions of computer random experiments performed using pseudo random numbers. Therefore, as pointed out Lehmann (2012), MCS methods are used whenever the functional relationships are analytically not tractable, as is the case for DS. This simulation technique based on the pioneering idea of Hekimoglu and Koch (1999) has been recently applied in geodesy.…”

Section: Preliminary Conceptsmentioning

confidence: 99%

“…Bulletin of Geodetic Sciences, 24(2): 152-170, Apr-Jun, 2018 example, Ryan and Lachapelle (2001) used simulations to obtain the minimal detectable bias polygon for the case of two outliers; Lehmann and Scheffler (2011) used MCS method to solve the problem how to determine the optimal levels of Type I error probabilities for global and local tests in DS; Lehmann (2012) used MCS method to improve the critical values of the test statistics; Niemeier and Tengen (2017) extended the classical concept of geodetic network adjustment by combining the uncertainty modeling and MCS.…”

Section: Preliminary Conceptsmentioning

confidence: 99%

“…Baarda, 1968;Pope, 1976;Berber and Hekimoglu, 2003;Lehmann, 2012). Therefore, the outlier model for q=1 is a n x 1 unit vector with 1 in its i th entry and zeros in the remaining (e.g.…”

Section: Preliminary Conceptsmentioning

confidence: 99%

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Design of Geodetic Networks Based on Outlier Identificationcriteria: An Example Applied to the Leveling Network

2018

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Abstract:We present a numerical simulation method for designing geodetic networks. The quality criterion considered is based on the power of the test of data snooping testing procedure. This criterion expresses the probability of the data snooping to identify correctly an outlier. In general, the power of the test is defined theoretically. However, with the advent of the fast computers and large data storage systems, it can be estimated using numerical simulation. Here, the number of experiments in which the data snooping procedure identifies the outlier correctly is counted using Monte Carlos simulations. If the network configuration does not meet the reliability criterion at some part, then it can be improved by adding required observation to the surveying plan. The method does not use real observations. Thus, it depends on the geometrical configuration of the network; the uncertainty of the observations; and the size of outlier. The proposed method is demonstrated by practical application of one simulated leveling network. Results showed the needs of five additional observations between adjacent stations. The addition of these new observations improved the internal reliability of approximately 18%. Therefore, the final designed network must be able to identify and resist against the undetectable outliers -according to the probability levels.Keywords: Reliability, Outlier, Numerical Simulation, Monte Carlo, Design of geodetic networks. Resumo:Nós apresentamos um método de simulação numérica para planejamento de redes geodésicas. O critério de qualidade considerado é baseado no poder do teste do procedimento estatístico data snooping. Esse critério expressa a probabilidade do procedimento data snooping de identificar corretamente um outlier. Em geral, o valor do poder do teste é sempre desconhecido na prática (definido na teoria). Porém, com o advento de computadores mais rápidos e sistemas de armazenamento de dados de maior capacidade, o poder do teste pode ser estimado por meio de simulações numéricas. O número de experimentos que o procedimento data snooping identifica corretamente um outlier é quantificado por meio do método Monte Carlo de simulação. Se a configuração inicial da rede não atender o critério de confiabilidade, então uma nova observação é adicionada no projeto da rede. O método não faz uso de observações reais coletadas em campo, dependendo apenas da configuração geométrica da rede, das incertezas das observações e da magnitude dos outliers. A eficiência do método é verificada por meio de um exemplo numérico de uma rede de nivelamento geométrico simulada. Os resultados mostraram a necessidade de cinco observações adicionais entre os pontos adjacentes. A adição destas novas observações melhorou a confiabilidade interna da rede de aproximadamente 18%. Portanto, a rede é projetada de modo que seja capaz de identificar outliers e ainda resistir a outilers não identificados nas observações -de acordo com os níveis de probabilidade.

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Section: Methods Proposal To Design Geodetic Networkmentioning

confidence: 99%

Section: Preliminary Conceptsmentioning

confidence: 99%

Section: Preliminary Conceptsmentioning

confidence: 99%

“…Baarda, 1968;Pope, 1976;Berber and Hekimoglu, 2003;Lehmann, 2012). Therefore, the outlier model for q=1 is a n x 1 unit vector with 1 in its i th entry and zeros in the remaining (e.g.…”

Section: Preliminary Conceptsmentioning

confidence: 99%

See 2 more Smart Citations

Design of Geodetic Networks Based on Outlier Identificationcriteria: An Example Applied to the Leveling Network

2018

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“…Note, that the kurtosis estimate might be affected with gross errors (Kukuča, 1967). Thus, before application of the signifi cance testing for β 1 and β 2 , it is advisable to detect outliers by applying any of the methods presented in (Barda,1968;Lehmann, 2012).…”

Section: Introductionmentioning

confidence: 99%

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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Monte Carlo Methods

Koch¹

2018

Handbuch Der Geodäsie

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Improved critical values for extreme normalized and studentized residuals in Gauss–Markov models

Cited by 70 publications

References 8 publications

Design of Geodetic Networks Based on Outlier Identificationcriteria: An Example Applied to the Leveling Network

Design of Geodetic Networks Based on Outlier Identificationcriteria: An Example Applied to the Leveling Network

MP estimation applied to platykurtic sets of geodetic observations

Monte Carlo Methods

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