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Journal of Geodetic Science

Editor-in-Chief: Eshagh, Mehdi

Open Access
Online
ISSN
2081-9943
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Vector regression introduced

Tik Mok
  • Dept. of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ H. Bâki Iz
  • Corresponding author
  • Dept. of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-06-06 | DOI: https://doi.org/10.2478/jogs-2014-0009

Abstract

This study formulates regression of vector data that will enable statistical analysis of various geodetic phenomena such as, polar motion, ocean currents, typhoon/hurricane tracking, crustal deformations, and precursory earthquake signals. The observed vector variable of an event (dependent vector variable) is expressed as a function of a number of hypothesized phenomena realized also as vector variables (independent vector variables) and/or scalar variables that are likely to impact the dependent vector variable. The proposed representation has the unique property of solving the coefficients of independent vector variables (explanatory variables) also as vectors, hence it supersedes multivariate multiple regression models, in which the unknown coefficients are scalar quantities. For the solution, complex numbers are used to rep- resent vector information, and the method of least squares is deployed to estimate the vector model parameters after transforming the complex vector regression model into a real vector regression model through isomorphism. Various operational statistics for testing the predictive significance of the estimated vector parameter coefficients are also derived. A simple numerical example demonstrates the use of the proposed vector regression analysis in modeling typhoon paths.

Keywords: complex least squares adjustment; vector data; vector regression

References

  • Anderson H. H., Hojbjerre M., Sorensen D. and Erikson P. S., 1995, Linear and Graphical Models, Springer-Verlag, New York.Google Scholar

  • Chinese National Meteorology Department - Shanghai Typhoon Research Institution Centre, 2012, China Typhoon Website. Available from: China, Chinese national meteorology department Web site: http://www.typhoon.gov.cn/index.php?controller=spage{&}pid=169[Accessed: May 14, 2012].Google Scholar

  • Elsner J.B. and Liu K.B., 2003, Examining the ENSO-typhoon hypothesis, CLIMATE RESEARCH, Vol. 25, pp. 43-54.Google Scholar

  • Kitamoto A., 2013, http://agora.ex.nii.ac.jp/~kitamoto, Research Organization of Information and Systems (ROIS) / National Institute of Informatics (NII) Department: Digital Content and Media Sciences Research Division.Google Scholar

  • NOAA, 2012, NOAA Earth System Research Laboratory. Available from: USA, NOAA Web site: http://www.esrl.noaa.gov/psd/data/ gridded/data.ncep.reanalysis.html [Accessed: May 14, 2012].Google Scholar

  • Rencher A.C., 1995, Multivariate Statistical Inference and Applications, John Wiley& Sons, New York.Google Scholar

  • Schneider D., 1982, Complex crustal strain approximation, Dept. of Surveying, University of New Brunswick, Fredericton.Google Scholar

  • Su B.K., 1988, Statistical Diagnosis and Forecast in Atmospheric Science, 1sted, Nanjing University, Jiang Su. ISBN: 7-305-00039-6.Google Scholar

  • Tobler W., 1994, Bidimensional regression. Geographical Analysis, 26, 187-212.Google Scholar

  • Wilson E.B., 1901, Vector Analysis, Yale University Press, pgs. 436.Google Scholar

About the article

Received: 2014-01-12

Accepted: 2014-04-04

Published Online: 2014-06-06

Published in Print: 2014-06-01


Citation Information: Journal of Geodetic Science, Volume 4, Issue 1, ISSN (Online) 2081-9943, DOI: https://doi.org/10.2478/jogs-2014-0009.

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© 2014 by H. Bâki Iz. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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