منابع مشابه
On Nonparametric Density Estimation in Sup-norm
The quality of estimation of a nonparametric density in the sup-norm strongly depends on the edge eeects. This is shown for the minimax Bahadur-type risk over a class of the HH older densities. The asymptotics of the Bahadur-type risks is compared with that for the traditional risks, and the links with the regression models are discussed.
متن کاملSup - norm Estimates in Glimm ’ s Method *
We give a proof that Total Variation {a,,(.)} < 1 can be replaced by Sup{u,(.)} e 1 in Glimm's method whenever a coordinate system of Riemann invariants is present. The argument is somewhat simpler but in the same spirit as that given by Glimm in his celebrated paper of 1965. 0 1990 Academic Press, Inc. We consider the Cauchy problem u, + F(u), = 0, (1) 4-G 0) = u,(x), (2) where (1) denotes a s...
متن کاملMaxiset in sup-norm for kernel estimators
In the Gaussian white noise model, we study the estimation of an unknown multidimensional function f in the uniform norm by using kernel methods. The performances of procedures are measured by using the maxiset point of view: we determine the set of functions which are well estimated (at a prescribed rate) by each procedure. So, in this paper, we determine the maxisets associated to kernel esti...
متن کاملA Note on the Sup Norm of Eisenstein Series
The sup norm problem has been an active area and now there exist non-trivial estimates for cusp forms of large level, on higher rank groups, and for half-integral weight forms [BH] [T1] [HT1] [HT2] [T2] [HRR] [BP] [BM] [M] [K]. Nevertheless, the basic estimate for Γ = PSL2(Z) in the eigenvalue aspect has not been improved. The case of Eisenstein series seems to have been largely neglected up to...
متن کاملSharp Estimation in Sup Norm with Random Design
Abstract. In this paper, we study the estimation of a function based on noisy inhomogeneous data (the amount of data can vary on the estimation domain). We consider the model of regression with random design, where the design density is unknown. We construct an asymptotically sharp estimator which converges, for sup norm error loss, with a spatially dependent normalisation which is sensitive to...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1963
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1963-10940-4