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A finite algorithm for the rank regression problem

Published online by Cambridge University Press:  14 July 2016

M. R. Osborne
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Abstract

A new approach to the minimization of polyhedral convex functions is applied to give a finite algorithm for the rank regression problem. Numerical results for the Daniel and Wood example are presented.

Keywords

RANK REGRESSIONDISPERSIONFINITE ALGORITHMDESCENT METHODPOLYHEDRAL CONVEX FUNCTIONSIGN SCORES
Type
Part 5 — Statistical Theory
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 241 - 252
Copyright
Copyright © 1982 Applied Probability Trust 

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References

Anderson, D. H. and Osborne, M. R. (1976) Discrete, linear, approximation problems in polyhedral norms. Numer. Math. 26, 179–189.CrossRefGoogle Scholar
Bloomfield, P. and Steiger, W. (1980) Least absolute deviation curve fitting. SIAM J. Statist. Comput. 1, 290–301.Google Scholar
Clark, D. I. (1981) Finite Algorithms for Optimisation Problems. Ph. D. Thesis, The Australian National University.Google Scholar
Clarke, D. I. and Osborne, M. R. (1982) Descent methods for minimising polyhedral convex functions.Google Scholar
Daniel, C. and Wood, F. S. (1971) Fitting Equations to Data. Wiley, New York.Google Scholar
Gill, P. E., Golub, G. H., Murray, W. and Saunders, M. A. (1974) Methods for modifying matrix factorizations. Math. Comput. 29, 505–535.Google Scholar
Hettmansperger, T. P. and Mckean, J. W. (1977) A robust alternative based on ranks to least squares in analyzing linear models. Technometrics 19, 275–284.Google Scholar
Jaeckel, L. A. (1972) Estimating regression coefficients by minimizing the dispersion of the residuals. Ann. Math. Statist. 43, 1449–1458.CrossRefGoogle Scholar
Lehmann, E. H. (1975) Nonparametrics. Holden-Day, San Francisco.Google Scholar
Moran, P. A. P. (1979) The use of rank correlation in large samples. Austral. J. Statist. 21, 293–300.Google Scholar
Osborne, M. R. (1981) Algorithms for discrete data parameter estimation problems. In Nonlinear Problems in Numerical Analysis , ed. Baker, C. T. H., Oxford University Press.Google Scholar
Rockafellar, R. T. (1970) Convex Analysis. Princeton University Press, Princeton, NJ.Google Scholar