WIAS Preprint No. 2061, (2015)

Two convergence results for an alternation maximization procedure


  • Andresen, Andreas
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62F10 62J12 62F25 62H12


  • profile maximum likelihood, local linear approximation, spread, local concentration, M-estimation, alternating procedure, EM algorithm




Andresen and Spokoiny's (2013) ``critical dimension in semiparametric estimation`` provide a technique for the finite sample analysis of profile M-estimators. This paper uses very similar ideas to derive two convergence results for the alternating procedure to approximate the maximizer of random functionals such as the realized log likelihood in MLE estimation. We manage to show that the sequence attains the same deviation properties as shown for the profile M-estimator in Andresen and Spokoiny (2013), i.e. a finite sample Wilks and Fisher theorem. Further under slightly stronger smoothness constraints on the random functional we can show nearly linear convergence to the global maximizer if the starting point for the procedure is well chosen.

Appeared in

  • J. Mach. Learn. Res., 17 (2016) pp. 1--53.

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