Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors

By O. Lepski, Enno Mammen, Vladimir Spokoiny. 1997

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Citations in the corpus

Kernel Mean Estimation via Spectral Filtering (2014, background): “Thus, one of the interesting future directions is to develop procedure that can adapt to this unknown parameter automatically.”
On the optimal estimation of probability measures in weak and strong topologies (2013, methodology): “A special case of this result is already proved in [34, 23] for D k when X is compact.”
Minimax or maxisets (2002, unknown): “dY n t = f(t)dt+ 1 √ n dWt, t ∈ [0, 1] (22)”
An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation (2009, methodology): “To do this, we slightly modify Lepski’s method for adaptive nonparametric density estimation (see [25], and further developments given, e.g., in [4, 26 ,27,33]).”
Adaptive density estimation: a curse of support? ✩ (2009, methodology): “In practice, the data are usually rescaled by the smallest and largest observations before performing any of the previous algorithms.”
Sharp Adaptive Estimation of Linear Functionals (2001, background): “Arguing as in Lepski, Mammen, and Spokoiny (1997), Goldenshluger and Nemirovskii (1997) one can deduce spatial adaptivity of such an estimator of a function from its pointwise adaptivity.”
On Spatial Adaptive Estimation of Nonparametric Regression (2004, background): “[2, 3], and Juditsky [4], adaptive kernel estimates of Lepskii, Mammen and Spokoiny [7]); in the cited papers, the smoothness of the signal is specified as membership in the Besov or Triebel spaces.”
Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes (2001, methodology): “To compare SARS with the HAS of Luo and Wahba (1997), smoothing splines, and MARS, we use examples considered by Luo and Wahba (1997, table 1); see Table 2 for the particular functions.”
Smoothing Quantile Regressions (2019, unknown): “First, uniformity in bandwidth is useful not only for adaptive bandwidth choices as in Lepski, Mammen, and Spokoiny (1997), but also for bandwidth-snooping-robust inference as in Armstrong and Koles´ar (2018).”