Abstract
The reduced rank regression model is a multivariate regression model with a coefficient matrix with reduced rank. The reduced rank regression algorithm is an estimation procedure which estimates the reduced rank regression model. It is related to canonical correlations and involves calculating eigenvalues and eigenvectors. We give a number of different applications to regression and time series analysis, and show how the reduced rank regression estimator can be derived as a Gaussian maximum likelihood estimator. We briefly mention asymptotic results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Bibliography
Anderson, T.W. 1951. Estimating linear restrictions on regression coefficients for multivariate normal distributions. Annals of Mathematical Statistics 22: 327–351.
Anderson, T.W., and H. Rubin. 1949. Estimation of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics 20: 46–63.
Bartlett, M.S. 1938. Further aspects of the theory of multiple regression. Proceedings of the Cambridge Philosophical Society 34: 33–40.
Box, G.E.P., and G.C. Tiao. 1977. A canonical analysis of multiple time series. Biometrika 64: 355–365.
Doornik, J.A., and R.J. O’Brien. 2002. Numerically stable cointegration analysis. Computational Statistics and Data Analysis 41: 185–193.
Engle, R.F., and C.W.J. Granger. 1987. Co-integration and error correction: Representation, estimation and testing. Econometrica 55: 251–276.
Engle, R.F., and S. Kozicki. 1993. Testing for common factors (with comments). Journal of Business Economics and Statistics 11: 369–378.
Hotelling, H. 1936. Relations between two sets of variables. Biometrika 28: 321–377.
Johansen, S. 1996. Likelihood based inference on cointegration in the vector autoregressive model. Oxford: Oxford University Press.
Reinsel, G.C., and R.P. Velu. 1998. Multivariate reduced rank regression. Lecture notes in statistics. New York: Springer.
Robinson, P.M. 1973. Generalized canonical analysis for time series. Journal of Multivariate Analysis 3: 141–160.
Author information
Authors and Affiliations
Editor information
Copyright information
© 2018 Macmillan Publishers Ltd.
About this entry
Cite this entry
Johansen, S. (2018). Reduced Rank Regression. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2682
Download citation
DOI: https://doi.org/10.1057/978-1-349-95189-5_2682
Published:
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-95188-8
Online ISBN: 978-1-349-95189-5
eBook Packages: Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences