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Journal of Geodetic Science

Editor-in-Chief: Eshagh, Mehdi

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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
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-06-06 | DOI: https://doi.org/10.2478/jogs-2014-0009


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


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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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