Staff Publications

Staff Publications

  • external user (warningwarning)
  • Log in as
  • language uk
  • About

    'Staff publications' is the digital repository of Wageningen University & Research

    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

    Full text documents are added when available. The database is updated daily and currently holds about 240,000 items, of which 72,000 in open access.

    We have a manual that explains all the features 

Record number 547525
Title Tracy-Widom statistic for the largest eigenvalue of autoscaled real matrices
Author(s) Saccenti, Edoardo; Smilde, Age K.; Westerhuis, Johan A.; Hendriks, Margriet M.W.B.
Source Journal of Chemometrics 25 (2011)12. - ISSN 0886-9383 - p. 644 - 652.
DOI https://doi.org/10.1002/cem.1411
Department(s) VLAG
Systems and Synthetic Biology
Publication type Refereed Article in a scientific journal
Publication year 2011
Keyword(s) Autoscaling - Covariance matrix - Eigenanalysis - Largest eigenvalue - Tracy-Widom distribution
Abstract

Eigenanalysis is common practice in biostatistics, and the largest eigenvalue of a data set contains valuable information about the data. However, to make inferences about the size of the largest eigenvalue, its distribution must be known. Johnstone's theorem states that the largest eigenvalues l1 of real random covariance matrices are distributed according to the Tracy-Widom distribution of order 1 when properly normalized to L1=l1-ηnpξnp, where ηnp and ξnp are functions of the data matrix dimensions n and p. Very often, data are expressed in terms of correlations (autoscaling) for which case Johnstone's theorem does not work because the normalizing parameters ηnp and ξnp are not theoretically known. In this paper we propose a semi-empirical method based on test-equating theory to numerically approximate the normalization parameters in the case of autoscaled matrices. This opens the way of making inferences regarding the largest eigenvalue of an autoscaled data set. The method is illustrated by means of application to two real-life data sets.

Comments
There are no comments yet. You can post the first one!
Post a comment
 
Please log in to use this service. Login as Wageningen University & Research user or guest user in upper right hand corner of this page.