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$$\ell_1$$ computation: An interior monologue. (English) Zbl 0933.62024
Dodge, Yadolah (ed.), $$L_1$$-statistical procedures and related topics. Papers of the 3rd international conference on $$L_1$$ norm and related methods held in Neuchâtel, Switzerland, August 11–15, 1997. Hayward, CA: IMS, Institute of Mathematical Statistics. IMS Lect. Notes, Monogr. Ser. 31, 15-32 (1997).
Summary: Some recent developments on the computation of least absolute error estimators are surveyed and a number of extensions to related problems are suggested. A very elementary example is used to illustrate the basic approach of “interior point” algorithms for solving linear programs. And a simple preprocessing approach for $$\ell_1$$ type problems is described. These developments, taken together, have the effect of dramatically improving the efficiency of absolute error computations, making them comparable to least squares methods even in massive datasets.
For the entire collection see [Zbl 0882.00044].

##### MSC:
 62G05 Nonparametric estimation 65C60 Computational problems in statistics (MSC2010) 62J05 Linear regression; mixed models
##### Keywords:
linear models; regression quantiles