Model selection via testing: an alternative to (penalized) maximum likelihood estimators

By Lucien Birgé. 2006

148 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f9214112cd43c3c91e24368a95006616e985b057

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In Computer Networks and Communications

In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Model Selection (2018, result): “Furthermore, Birgé (2006) derives results similar to (23)–(25) for model selection based on preliminary tests.”
Robust machine learning by median-of-means: Theory and practice (2017, methodology): “ pay is that the function to be minimized is not convex and is therefore hard to implement. The idea of estimation by aggregation of tests is due to Le Cam [48,49] and was further developed by Birge [15], Baraud [11], Baraud, Birge and Sart [10]. MOM estimators have been recently considered see [60,”
Parametric or nonparametric? A parametricness index for model selection (2011, background): “Theoretically speaking, the essential difference between parametric and nonparametric scenarios in our context is that the best model has no approximation error for the former and all the candidate models have nonzero approximation errors for the latter.”
On adaptive posterior concentration rates (2013, unknown): “By “geometry”, we simply mean here the existence of a tractable (pre)-metric d that controls the statistical distance between parameters: this can be the Hellinger distance used in the Birgé-Le Cam testing theory in density estimation or simply the L2-distance in Gaussian white noise model linked t”
ROBUST EMPIRICAL MEAN ESTIMATORS (2011, methodology): “[3] provides a general approach including density estimation but his procedure based on pairwise tests between estimators, in the spirit of [8] was not com-ROBUST putationally tractable.”
Convergence rates of posterior distributions for non-i.i.d. observations (2007, background): “[5]) that the like lihood ratio test for /o versus f\ satisfies the conclusion of Lemma 2 relative to || ||? (instead of dn and 0,= /).”
Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator (2015, background): “From Proposition 5 of [5] we have that the test 1l (”
Learning from MOM’s principles: Le Cam’s approach (2017, methodology): “Another line of research to build robust estimators and robust selection procedures was initiated by Le Cam (1973, 1986) and further developed by Birg´e (2006), Baraud (2011) and Baraud et al. (2017).”
Aggregation for Gaussian regression (2007, background): “4) in regression problems have been obtained by many authors mainly for the model selection case; see, for example, [4, 5, 7, 8, 9, 10, 11, 12, 15, 23, 28, 30, 32, 42] and the references cited in these works.”
Parametric estimation. Finite sample theory (2011, methodology): “We mention the papers Van de Geer (1993), Birgé and Massart (1993), Birgé and Massart (1998), Birgé (2006) and references therein.”
From Local Kernel to Nonlocal Multiple-Model Image Denoising (2009, background): “A ﬂow of publications on aggregation can be seen in mathematical statistics (e.g., Birge 2006; Bunea et al. 2007; Goldenshluger 2009).”