2015/01/07 by Andreas Andresen, Andresen, Andreas, Vladimir Spokoiny +1
Decision Sciences · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Fractional Differential Equations Solutions #Probabilistic and Robust Engineering Design #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1501.01525
openalex publication_date 2015/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.