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A robust biplot
Author(s) -
Daigle Gaétan,
Rivest LouisPaul
Publication year - 1992
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315312
Subject(s) - biplot , principal component analysis , mathematics , covariance matrix , statistics , univariate , data matrix , population , multivariate statistics , biology , clade , biochemistry , demography , sociology , gene , genotype , phylogenetic tree
This paper introduces a robust biplot which is related to multivariate M ‐estimates. The n × p data matrix is first considered as a sample of size n from some p ‐variate population, and robust M ‐estimates of the population location vector and scatter matrix are calculated. In the construction of the biplot, each row of the data matrix is assigned a weight determined in the preliminary robust estimation. In a robust biplot, one can plot the variables in order to represent characteristics of the robust variance‐covariance matrix: the length of the vector representing a variable is proportional to its robust standard deviation, while the cosine of the angle between two variables is approximately equal to their robust correlation. The proposed biplot also permits a meaningful representation of the variables in a robust principal‐component analysis. The discrepancies between least‐squares and robust biplots are illustrated in an example.