Asymptotic normality of plug-in level set estimates.

By David Mason, Wolfgang Polonik. 2009

97 citations recorded by the source corpus.

We establish the asymptotic normality of the $G$-measure of the symmetric difference between the level set and a plug-in-type estimator of it formed by replacing the density in the definition of the level set by a kernel density estimator. Our proof will highlight the efficacy of Poissonization methods in the treatment of large sample theory problems of this kind.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ffa95b85aaec6589517ad07cb521a31e2c9c2335

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES (2013, background): “(See Mason and Polonik (2009) for details.”
A Review on Modal Clustering (2016, background): “…are Tsybakov (1997), Walther (1997), Cuevas et al. (2000), Baíllo et al. (2000), Baíllo et al. (2001), Baíllo (2003), Rigollet & Vert (2009) and Mason & Polonik (2009), and references therein, which delineate conditions, rates of convergence and further asymptotic results for a level-set…”
Testing functional inequalities (2011, background): “…kernel estimation of a polarization measure; Lee and Whang (2009) established asymptotic null distributions for the L1-type test statistics for conditional treatment effects; and Mason (2009) established both finite sample and asymptotic moment bounds for the Lp risk for kernel density estimators.”
On Statistical Properties of Sets Fulfilling Rolling-Type Conditions (2011, background): “See [3], [4], and [18] for some recent interesting examples.”