Estimation des densités: risque minimax

By J. Bretagnolle, C. Huber. 1978

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Metalearners for estimating heterogeneous treatment effects using machine learning (2017, background): “2 Reducing transphobia: A field experiment on doorto-door canvassing In an experiment that received wide-spread media attention, Broockman and Kalla (2016) show that brief (10 minute) but high quality door-to-door conversations can markedly reduce prejudice against non-gender conforming individuals ”
On minimax density estimation on R (2001, methodology): “A closely related notion of spacing selection for Bsplines Bayesian density estimator was implemented in Ciesielski and Kamont (1999) – cf. also the adaptive window selection procedure for kernel estimators in Juditsky and Nazin (2001) and Butucea (2000).”
Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons (2023, background): “And the last inequality is due to the Bretagnolle–Huber inequality Bretagnolle and Huber (1979).”
On adaptive minimax density estimation on $$R^d$$Rd (2012, methodology): “The minimax and adaptive minimax density estimation with Lp–loss is a subject of the vast literature, see for example Bretagnolle and Huber (1979), Ibragimov and Khasminskii (1980, 1981), Devroye and Györfi (1985), Devroye and Lugosi (1996, 1997, 2001), Efroimovich (1986, 2008), Hasminskii and…”
On f-Divergences: Integral Representations, Local Behavior, and Inequalities (2018, methodology): “This approach leads to generalizations of the Bretagnole-Huber inequality [6], whose generalizations are later motivated in this section.”
Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions (2009, methodology): “These inequalities have applications in nonparametric statistics, as proved in [ 2 ].”
Rosenthal-type inequalities for the maximum of partial sums of stationary processes and examples (2011, background): “k=1 Ek−1(X 2 k) ∥∥1/2 p/2 for any p ≥ 2, (2)”
Bandit Algorithms (2020, methodology): “2 is also known as the Bretagnolle–Huber inequality [Bretagnolle and Huber, 1979].”
Near optimal thresholding estimation of a Poisson intensity on the real line (2008, background): “3 proves that the convenient choice for γ belongs to the interval [1, 12].”
Inequalities and limit theorems for weakly dependent sequences (2013, methodology): “We refer to Davydov (1973) and to Bradley (1986) for a proof of this result.”
Smooth Discrimination Analysis (1999, methodology): “We use Assouad's lemma [see Bretagnolle and Huber (1979) andAssouad (1983)].”
Adaptive nonparametric confidence sets (2006, unknown): “ar X iv :m at h/ 06 05 47 3v 1 [ m at h. ST ] 1 7 M ay 2 00 6 The Annals of Statistics 2006, Vol. 34, No. 1, 229–253 DOI: 10.1214/009053605000000877 c© Institute of Mathematical Statistics, 2006”