Formulas for robust, one-pass parallel computation of covariances and arbitrary-order statistical moments.

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We present a formula for the pairwise update of arbitrary-order centered statistical moments. This formula is of particular interest to compute such moments in parallel for large-scale, distributed data sets. As a corollary, we indicate a specialization of this formula for incremental updates, of particular interest to streaming implementations. Finally, we provide pairwise and incremental update formulas for the covariance. Centered statistical moments are one of the most widely used tools in descriptive statistics. It is therefore essential for statistical analysis packages that robust and efficient algorithms be devised and implemented. However, robustness and speed of execution, in this context ... continued below

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18 p.

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Pebay, Philippe Pierre September 1, 2008.

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Description

We present a formula for the pairwise update of arbitrary-order centered statistical moments. This formula is of particular interest to compute such moments in parallel for large-scale, distributed data sets. As a corollary, we indicate a specialization of this formula for incremental updates, of particular interest to streaming implementations. Finally, we provide pairwise and incremental update formulas for the covariance. Centered statistical moments are one of the most widely used tools in descriptive statistics. It is therefore essential for statistical analysis packages that robust and efficient algorithms be devised and implemented. However, robustness and speed of execution, in this context as well as in others, tend to be orthogonal. For instance, it is well known1 that algorithms for calculating centered statistical moments that utilize sum of powers for the sake of execution speed (one-pass algorithms) lead to unacceptable numerical instability.

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18 p.

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  • Report No.: SAND2008-6212
  • Grant Number: AC04-94AL85000
  • DOI: 10.2172/1028931 | External Link
  • Office of Scientific & Technical Information Report Number: 1028931
  • Archival Resource Key: ark:/67531/metadc837537

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  • September 1, 2008

Added to The UNT Digital Library

  • May 19, 2016, 3:16 p.m.

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  • Dec. 9, 2016, 8:07 p.m.

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Pebay, Philippe Pierre. Formulas for robust, one-pass parallel computation of covariances and arbitrary-order statistical moments., report, September 1, 2008; United States. (digital.library.unt.edu/ark:/67531/metadc837537/: accessed June 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.