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By Eric A. Cator, Cor Kraaikamp, Hendrik P. Lopuhaa, Jon A. Wellner, Geurt Jongbloed

Cator E.A., et al. (eds.) Asymptotics.. debris, approaches and inverse difficulties (Inst.Math.Stat., 2007)(ISBN 0940600714)-o

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7) that the problem of estimating µ with T-estimators always reduces to intensity estimation once a reference measure λ has been chosen. 8) shows that the performance of the estimator sˆ(X) is connected to the choice of the models in L+ 1 (λ), the component µ⊥ (X ) of the risk depending only on λ. We might as well assume that µ⊥ (X ) is known since this would not change anything concerning the performance of the T-estimators for a given λ. This is why we shall essentially focus, in the sequel, on intensity estimation.

2 inf √ s−t t∈S m 2 + ηm . 3) are satisfied so that Theorem 3 applies. 7). 2. About the computation of T-estimators We already mentioned that the relevance of T-estimators is mainly of a theoretical nature because of the difficulty of their implementation. Let us give √ here a simple illustrative example based on a single linear approximating space S for s, of dimension k. To try to get a practical implementation, we shall use a simple discretization strategy. The first step is to replace S, that we identify to Rk via the choice of a basis, by θZk .

6] Dubeau, F. and Savoie, J. (1997). Best error bounds for odd and even degree deficient splines. SIAM J. Numer. Anal. 34 1167–1184. , Rufibach, K. and Wellner, J. A. (2007). Marshall’s lemma [7] Du for convex density estimation. In Asymptotics, Particles, Processes, and Inverse Problems, IMS Lecture Notes Monogr. Ser. Inst. Math. , Beachwood, OH. To appear. [8] Durot, C. -S. (2003). On the distance between the empirical process and its concave majorant in a monotone regression framework. Ann.

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