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Title: Vector regression introduced
Authors: Mok, T
Iz, HB 
Keywords: Complex least squares adjustment
Vector data
Vector regression
Issue Date: 2014
Publisher: De Gruyter Open Ltd
Source: Journal of geodetic science, June 2014, v. 4, no. 1, p. 57-64 How to cite?
Journal: Journal of geodetic science 
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.
ISSN: 2081-9919 (print)
2081-9943 (online)
DOI: 10.2478/jogs-2014-0009
Rights: © 2014 Tik Mok and H. Bâki Iz, licensee De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0),
The following publication Tik, M. & Iz, H. B. (2014). Vector regression introduced. Journal of Geodetic Science, 4 (1), 57-64 is available at
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