Geometric approach to statistical analysis on the simplex

  • V. Pawlowsky-Glahn
  • J. J. Egozcue

DOI: 10.1007/s004770100077

Cite this article as:
Pawlowsky-Glahn, V. & Egozcue, J. Stochastic Environmental Research and Risk Assessment (2001) 15: 384. doi:10.1007/s004770100077

Abstract.

 The geometric interpretation of the expected value and the variance in real Euclidean space is used as a starting point to introduce metric counterparts on an arbitrary finite dimensional Hilbert space. This approach allows us to define general reasonable properties for estimators of parameters, like metric unbiasedness and minimum metric variance, resulting in a useful tool to better understand the logratio approach to the statistical analysis of compositional data, who's natural sample space is the simplex.

Key words: Aitchison geometry, compositional data, Euclidean space, finite dimensional Hilbert space, metric center, metric variance. 

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • V. Pawlowsky-Glahn
    • 1
  • J. J. Egozcue
    • 2
  1. 1.Dept. d'Informàtica i Matemàtica Aplicada, Universitat de Girona, Campus Montilivi – P-1, E-17071 Girona, Spain e-mail: vera.pawlowsky@udg.esES
  2. 2.Dept. de Matemàtica Aplicada III, ETSECCPB, Universitat Politècnica de Catalunya, Barcelona, SpainES

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