BLU Estimators and Compositional Data

By Vera Pawlowsky-Glahn, Juan José Egozcue. 2002

123 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Global and Planetary Change, Media Technology

View Paper: https://www.semanticscholar.org/paper/d98d0900a7a5203b96d984c3b8f08accf683af88

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Citations in the corpus

Hilbert Space of Probability Density Functions Based on Aitchison Geometry (2006, background): “On the basis of an early work by Aitchison [1, 2], it was completed only recently, when the Aitchison distance in the simplex was associated with an inner product—leading to the recognition of a finite-dimensional Hilbert space structure [3, 4, 5 ]—and orthonormal bases were identified [6].”
Dealing with Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation (2003, background): “See Aitchison (2002), Billheimer, Guttorp, and Fagan (2001) and Pawlowsky-Glahn and Egozcue (2001, 2002) for further details.”
Compositional Data Analysis: Where Are We and Where Should We Be Heading? (2005, methodology): “We refer to this as the finite dimensional Hilbert space structure of the simplex, in order to distinguish it from the ordinary Euclidean structure of real spaces (Billheimer, Guttorp, and Fagan, 1997, 2001; Egozcue and others, 2003; Pawlowsky-Glahn and Egozcue, 2001, 2002 ).”
Imputation of missing values for compositional data using classical and robust methods (2010, background): “Here, one has to correct the geometric mean by the ratio of the sum of the parts of the incomplete observation and the sum of the elements of the geometric mean vector (center of compositional data set, see Pawlowsky-Glahn and Egozcue, 2002 ).”
Exploring Compositional Data with the CoDa-Dendrogram (2011, methodology): “Once the sample space is identified as the simplex S9 with its Aitchison geometry, the first statistical elements, namely the mean and variance-covariance, can also be identified (Aitchison, 1997; Pawlowsky-Glahn and Egozcue, 2001, 2002).”
Bayesian-multiplicative treatment of count zeros in compositional data sets (2015, background): “This particularity is corroborated by the total log-ratio variability (e.g., Pawlowsky-Glahn and Egozcue, 2002) of the threepart subcomposition for only those 25 sows with at least one zero in these parts.”
Bayes linear spaces (2010, background): “…Received: February 2010 Accepted: October 2010 group operation, and its Euclidean structure has been completed (Billheimeret al., 2001; Pawlowsky-Glahn and Egozcue, 2001, 2002; Egozcueet al., 2003) The extension of the underlying ideas to compositions of infinitely many parts is due…”