Least Absolute Deviations: Theory, Applications and Algorithms

Least Absolute Deviations: Theory, Applications and Algorithms By Peter Bloomfield
Publisher: Bir kha user 1984 | 349 Pages | ISBN: 3764331577 , 0817631577 | DJVU | 3 mb



Least squares is probably the best known method for fitting linear models and by far the most widely used. Surprisingly, the discrete L1 analogue, least absolute deviations (LAD) seems to have been considered first. Possibly the LAD criterion was forced into the background because of the computational difficulties associated with it.
Recently there has been a resurgence of interest in LAD. It was spurred on by work that has resulted in efficient algorithms for obtaining LAD fits. Another stimulus came from robust statistics. LAD estimates resist undue effects from a few, large errors. Therefore, in addition to being robust, they also make good starting points for other iterative, robust procedures.
The LAD criterion has great utility. LAD fits are optimal for linear regressions where the errors are double exponential. However they also have excellent properties well outside this narrow context. In addition they are useful in other linear situations such as time series and multivariate data analysis. Finally, LAD fitting embodies a set of ideas that is important in linear optimization theory and numerical analysis.


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