Fast communication: On maximum likelihood estimation in factor analysis-An algebraic derivation

  • Authors:

  • Petre Stoica;Magnus Jansson

  • Affiliations:

  • Division of Systems and Control, Department of Information Technology, Uppsala University, Uppsala, Sweden;ACCESS Linnaeus Center, Electrical Engineering, KTH-Royal Institute of Technology, SE-100 44 Stockholm, Sweden

  • Venue:
  • Signal Processing
  • Year:
  • 2009

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Abstract

The maximum likelihood estimate in factor analysis is typically obtained as the solution of the stationary point equation of the likelihood function. This type of derivation suffers from two problems: it is rather cumbersome and, in fact, it is incomplete as it does not include a proof that the so-obtained estimate is indeed a global maximum point of the likelihood function. In this note we present a simple algebraic derivation of the maximum likelihood estimate in factor models with spherical noise that applies to the general complex-valued data case.