Nonparametric density estimation : the L[1] view

By Luc Devroye, László Györfi. 1987

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Citations in the corpus

On the optimal estimation of probability measures in weak and strong topologies (2013, background): “timator, which under suitable conditions are shown to be optimal with respect to the Lr loss (1 ≤ r≤ ∞) in the sense of achieving the minimax rate over all estimators for densities in certain classes [9, 22, 40]. Therefore, depending on whether P has a density or not, there are two diﬀerent estimato”
Robust Estimators in High Dimensions without the Computational Intractability (2016, neutral): “Our results fit in the framework of density estimation, a classical problem in statistics with a rich history and extensive literature (see e.g., [27], [28], [29], [30], [31]).”
Hadamard Response: Estimating Distributions Privately, Efficiently, and with Little Communication (2018, background): “The problem has a rich, and vast literature (see e.g. [6, 39, 17, 18], and many others), with the primary goal of statistical eﬃciency, namely minimizing the sample complexity for estimation, which is the ﬁrst resource we consider.”
On adaptive minimax density estimation on $$R^d$$Rd (2012, background): “…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 Ibragimo (1990), Donoho et al. (1996),…”
Nonparametric Density Estimation: Toward Computational Tractability (2003, background): “i.e. as more data are observed, the estimate converges to the true density [ 5 ].”
Maximum likelihood estimation of a multi‐dimensional log‐concave density (2008, background): “Our first proposition below is intended to give some insight into this issue.”
A kernel type nonparametric density estimator for decompounding (2005, background): “Properties of kernel estimators can be found in recent books such as Devroye and Gy¨o r fi [6], Prakasa Rao [12], Tsybakov [16] and Wand and Jones [19].”