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See detailROBUST BAYES-LIKE ESTIMATION: RHO-BAYES ESTIMATION
Baraud, Yannick UL; Birgé, Lucien

in Annals of Statistics (2020)

We observe n independent random variables with joint distribution P and pretend that they are i.i.d. with some common density s (with respect to a known measure μ) that we wish to estimate. We consider a ... [more ▼]

We observe n independent random variables with joint distribution P and pretend that they are i.i.d. with some common density s (with respect to a known measure μ) that we wish to estimate. We consider a density model S for s that we endow with a prior distribution π (with support in S) and build a robust alternative to the classical Bayes posterior distribution which possesses similar concentration properties around s whenever the data are truly i.i.d. and their density s belongs to the model S. Furthermore, in this case, the Hellinger distance between the classical and the robust posterior distributions tends to 0, as the number of observations tends to infinity, under suitable assumptions on the model and the prior. However, unlike what happens with the classical Bayes posterior distribution, we show that the concentration properties of this new posterior distribution are still preserved when the model is misspecified or when the data are not i.i.d. but the marginal densities of their joint distribution are close enough in Hellinger distance to the model S. [less ▲]

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See detailOn partial-sum processes of ARMAX residuals
Holcblat, Benjamin UL; Gronneberg, Steffen

in Annals of Statistics (2019), 47(6), 3216-3243

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See detailRho-estimators revisited: general theory and applications
Baraud, Yannick UL; Birgé, Lucien

in Annals of Statistics (2018), 46(6B), 3767--3804

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See detailGaussian model selection with an unknown variance
Baraud, Yannick UL; Giraud, Christophe; Huet, Sylvie

in Annals of Statistics (2009), 37(2), 630--672

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See detailAsymptotics for posterior hazards
De Blasi, Pierpaolo; Peccati, Giovanni UL; Igor, Prünster

in Annals of Statistics (2009), 37(4), 1906--1945

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See detailTesting convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function
Baraud, Yannick UL; Huet, Sylvie; Laurent, Béatrice

in Annals of Statistics (2005), 33(1), 214--257

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See detailConfidence balls in Gaussian regression
Baraud, Yannick UL

in Annals of Statistics (2004), 32(2), 528--551

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See detailAdaptive tests of linear hypotheses by model selection
Baraud, Yannick UL; Huet, S.; Laurent, B.

in Annals of Statistics (2003), 31(1), 225--251

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See detailTesting Condtional Moment Restrictions
Tripathi, Gautam UL; Kitamura, Yuichi

in Annals of Statistics (2003), 31

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See detailAdaptive estimation in autoregression or $\beta$-mixing regression via model selection
Baraud, Yannick UL; Comte, F.; Viennet, G.

in Annals of Statistics (2001), 29(3), 839--875

Detailed reference viewed: 91 (11 UL)