Uniform in Bandwidth Estimation of Integral Functionals of the Density Function

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Empirical estimation of entropy functionals with confidence (2010, background): “These include consistent estimators based on entropic graphs [19, 36], gap estimators [43], nearest neighbor distances [17, 26, 29, 45], kernel density plug-in estimators [1, 11, 3, 18, 4, 16], Edgeworth approximations [21], convex risk minimization [35] and orthogonal projections [25].”
Limit theorems for empirical processes of cluster functionals (2009, methodology): “For the analysis of such processes for i.i.d. data we refer to Einmahl (1997), Giné, Mason and Zaitsev (2003) and Giné and Mason (2008) and to the lists of references in these papers.”
On local U-statistic processes and the estimation of densities of functions of several sample variables (2007, background): “See also Bickel and Ritov [4] or Gine and Mason [19] and references therein for other */n consis tent estimators of f f2ix)dx.”