Geodesic
Defining a Unique Median via Minimizing Families of Norms
Journal of convex analysis, Tome 24 (2017) no. 1, pp. 199-212
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

It is well-known that the median of an even number of datapoints is not unique; by any of many equivalent definitions, any point in the interval between the innermost points qualify. Recalling that the mean can be defined by a least squares approximation to the dataset, the median via least absolute differences, we consider minimizing the Lp norm from the dataset to the diagonal, and compute its limit as p approaches 1 from the right side --- the result is not the midpoint as typically used. We also construct a different family of strictly convex norms converging to L1 exhibiting a different limit-median. 
@article{JCA_2017_24_1_JCA_2017_24_1_a14,
     author = {J. Tsang and R. Pereira},
     title = {Defining a {Unique} {Median} via {Minimizing} {Families} of {Norms}},
     journal = {Journal of convex analysis},
     pages = {199--212},
     year = {2017},
     volume = {24},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a14/}
}
TY  - JOUR
AU  - J. Tsang
AU  - R. Pereira
TI  - Defining a Unique Median via Minimizing Families of Norms
JO  - Journal of convex analysis
PY  - 2017
SP  - 199
EP  - 212
VL  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a14/
ID  - JCA_2017_24_1_JCA_2017_24_1_a14
ER  - 
%0 Journal Article
%A J. Tsang
%A R. Pereira
%T Defining a Unique Median via Minimizing Families of Norms
%J Journal of convex analysis
%D 2017
%P 199-212
%V 24
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a14/
%F JCA_2017_24_1_JCA_2017_24_1_a14
J. Tsang; R. Pereira. Defining a Unique Median via Minimizing Families of Norms. Journal of convex analysis, Tome 24 (2017) no. 1, pp. 199-212. http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a14/