Computational Algorithms for Calculating Least Absolute Value and Chebyshev Estimates for Multiple Regression

SYNOPTIC ABSTRACT

Least absolute value (LAV) and Chebyshev estimation are two possible alternatives to least squares estimation in multiple regression models. This paper reviews the historical development of these two alternatives with special attention placed on the development of algorithms for producing LAV and Chebyshev estimates of the regression parameters. Recent algorithmic improvements are reviewed, sources for obtaining computer programs are identified and recommendations are made for the most efficient algorithm for specific cases. In the final section suggestions for future research are made for the development and refinement of computational algorithms and inference procedures.

Key Words and Phrases:

• minimum absolute deviation estimation
• L₁-norm estimation
• L_∞-norm estimation
• linear programming
• optimization