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Bulletin géodésique

, Volume 68, Issue 3, pp 162–167 | Cite as

Criteria for internal reliability of linear least squares models

  • W. Prószyński
Article

Abstract

An approach to analysis of internal reliability of linear least squares models is presented. It is based on the relationship between a single observational disturbance, i.e. a gross error or a blunder, and the model response being a certain pattern of distortions in the least squares residuals. Rigorous formulae describing this relationship in terms of internal reliability characteristics are derived both for the models with uncorrelated and correlated observations. A specific case of decorrelated observations is also taken into consideration. Finally, the criteria for the evaluation of the model internal reliability are proposed for all the above cases. It is worth mentioning that the criteria are obtained without resorting to any particular method of statistical testing. The theory is illustrated with two numerical examples, using simple measuring schemes.

Keywords

Model Response Internal Reliability Local Response Reliability Level Reliability Criterion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Cooper MA (1987) Control Surveys in Civil Engineering. Collins, LondonGoogle Scholar
  2. Cross PA (1983) Advanced least squares applied to position fixing. Working Paper No 6, Department of Land Surveying, North East London Polytechnic, 205 pp.Google Scholar
  3. Pelzer H (1979) Criteria for the reliability of networks. Optimisation of Design and Computation of Control Networks, Budapest, Akademai Kiado, pp 553–562Google Scholar
  4. Pelzer H (1985) Geodaetische Netze in Landes- und Ingenieurvermessung II. Stuttgart, Konrad Wittwer, pp 147–152Google Scholar
  5. Nowak E, Prószyński W (1990) Interactive system for solving horizontal positioning problems in Engineering Surveys. Proceedings of XIX FIG Congress, Helsinki, Finland, pp 608/2.1–608/2.7Google Scholar
  6. Prószyński W (1990) Transformations of the reference system in engineering survey networks. Manuscripta Geodaetica 15:315–324Google Scholar
  7. Prószyński W (1992) Twierdzenie Otrębskiego a niezawodność sieci (The Otrębski's Theorem and Reliability of Networks). Geodezja i Kartografia, t.XLI, z.1/2:7–17Google Scholar
  8. Rao CR (1982) Modele liniowe statystyki matematycznej. Państwowe Wydawnictwa Naukowe, WarszawaGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • W. Prószyński
    • 1
  1. 1.Institute of Applied GeodesyWarsaw University of TechnologyWarszawaPoland

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