Abstract
The use of the L 1-norm via the least absolute deviations appeared early in the field of statistics. Generally people mention Boscovich (1757) and Laplace (1793), and for further historical aspects the reader will may consult Farebrother (1987). However, many periods of silence followed those pioneering works. There are many reasons for this lack of development. In particular, some computational difficulties arose in the city-block approaches. During the last two decades, we note a growing interest in statistical methods based upon the L 1-norm. This phenomenon concerns many areas such as robustness, nonparametric analysis, multidimensional scaling. In this last field, dimensionality problems are crucial. This chapter is devoted to theoretical and computational results on the dimension of an L 1-figure.
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Fichet, B. (1994). Dimensionality problems in L 1-norm representations. In: Van Cutsem, B. (eds) Classification and Dissimilarity Analysis. Lecture Notes in Statistics, vol 93. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2686-4_8
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DOI: https://doi.org/10.1007/978-1-4612-2686-4_8
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