Abstract
Using a few very basic observations, we proposed recently a direct and finite algorithm for the computation of the l ∞ regression line on a discrete set \(\left\{ {(x_i ,y_i )} \right\}_i^n \) under the assumption that \(x_1 < x_2 < \cdots < x_n \) In this paper, we extend the algorithm to the case with at least one, possibly multiple y-values for each distinct x_i. Our algorithm finds all the regression lines in O(n 2) operations in the worst-case scenario and improves the existing best-known computational complexity result for this problem. Numerical results on random problems are included.
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References
SPRENT, P., Models in Regression and Related Topics, Methuen and Company, London, England, 1969.
FOLEY, R., and FRAZELLE, E., Analytical Results for Miniload Throughput and the Distribution of Dual Command Trauel Times, IEE Transactions, Vol. 23, pp. 273–281, 1991.
GIBSON, D. R., and PULAPAKA, H., An Algorithm for Log Rotation in Sawmills, Wood and Fiber Science, Vol. 31, pp. 192–199, 1999.
BARRODALE, I., and YOUNG, A., Algorithms for Best L??and LS Linear Approximation on a Discrete Set, Numerische Mathematik, Vol. 8, pp. 295–306, 1966.
BARTELS, R. H., CONN, A. R., and CHARALAMBOUS, C., On the Cline Direct Method for Soluing Ouerdetermined Linear Systems in the lS Sense, SIAM Journal on Numerical Analysis, Vol. 15, pp. 255–270, 1978.
RICE, J., The Approximation of Functions, Vol. 1: Linear Theory, Addison-Wesley, Reading, Massachusetts, 1964.
SHAMOS, M., Geometry and Statistics: Problems at the Interface, Algorithms and Complexity: New Directions and Recent Results, Edited by J. F. Traub, Academic Press, New York, NY, pp. 251–280, 1976.
JI, J., and KICEY, C., An Efficient Method for lS Regression, Working Paper, Department of Mathematics and Computer Science, Valdosta State University, 2000.
MAHLER, H., A Graphical Illustration of Experience Rating Credibilities, Proceedings of the Casualty Actuarial Society, Vol. 85, pp. 654–688, 1998.
HOARE, C., Quicksort, Computer Journal., Vol. 5, pp. 10–15, 1962.
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Ji, J., Kicey, C. An Algorithm for l∞ Regression with Quadratic Complexity. Journal of Optimization Theory and Applications 112, 561–574 (2002). https://doi.org/10.1023/A:1017916132749
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DOI: https://doi.org/10.1023/A:1017916132749