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ROBUST BAYES-LIKE ESTIMATION: RHO-BAYES ESTIMATION Baraud, Yannick ; 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 ▲] Detailed reference viewed: 185 (49 UL)On partial-sum processes of ARMAX residuals Holcblat, Benjamin ; in Annals of Statistics (2019), 47(6), 3216-3243 Detailed reference viewed: 32 (4 UL)Rho-estimators revisited: general theory and applications Baraud, Yannick ; in Annals of Statistics (2018), 46(6B), 3767--3804 Detailed reference viewed: 210 (38 UL)Gaussian model selection with an unknown variance Baraud, Yannick ; ; in Annals of Statistics (2009), 37(2), 630--672 Detailed reference viewed: 92 (10 UL)Asymptotics for posterior hazards ; Peccati, Giovanni ; in Annals of Statistics (2009), 37(4), 1906--1945 Detailed reference viewed: 162 (0 UL)Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function Baraud, Yannick ; ; in Annals of Statistics (2005), 33(1), 214--257 Detailed reference viewed: 87 (6 UL)Confidence balls in Gaussian regression Baraud, Yannick in Annals of Statistics (2004), 32(2), 528--551 Detailed reference viewed: 110 (7 UL)Adaptive tests of linear hypotheses by model selection Baraud, Yannick ; ; in Annals of Statistics (2003), 31(1), 225--251 Detailed reference viewed: 87 (7 UL)Testing Condtional Moment Restrictions Tripathi, Gautam ; in Annals of Statistics (2003), 31 Detailed reference viewed: 52 (3 UL)Adaptive estimation in autoregression or $\beta$-mixing regression via model selection Baraud, Yannick ; ; in Annals of Statistics (2001), 29(3), 839--875 Detailed reference viewed: 97 (12 UL) |
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