Abstract
This paper gives a rather general view on the L1 norm criterion on the area of data analysis and related topics. We tried to cover all aspects of mathematical properties, historical development, computational algorithms, simultaneous equations estimation, statistical modeling, and application of the L1 norm in different fields of sciences.
Highlights
The L1norm is an old topic in science, lack of a general book or paper on this subject induced me to gather a relatively complete list of references in this paper
Since each of these hyperplanes corresponds to a particular m subset of observations, there will be m observations that lie on the regression hyperplane (see, Taylor (1974))
The essence of the algorithms which fall within this category is finding a steep path to descend down the polyhedron of the L1norm regression objective function
Summary
The L1norm is an old topic in science, lack of a general book or paper on this subject induced me to gather a relatively complete list of references in this paper. Least absolute errors estimator is very old, it has emerged in the literature again and has attracted attention in the last two decades because of unsatisfactory properties of least squares This method is discussed in econometrics textbooks such as Kmenta (1986) and Maddala (1977). Bassett (1973), Forth (1974), Anderson (1975), Ronner (1977), Nyquist (1980), Clarke (1981), Kotiuga (1981), Gonin (1983), Busovaca (1985), Kim ( ), Bidabad (1989a,b) which are more recent (see bibliography for the corresponding departments and universities) Robust property of this estimator is its advantage to deal with large variance error distributions. When the model is enlarged, and equations enter simultaneously, difficulties of computation increase Another problem with this estimator is that the properties of the solution space is not completely clear, and the corresponding closed form of the solution have not been derived yet.
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