Optimal rates for plug-in estimators of density level sets
نویسندگان
چکیده
منابع مشابه
Optimal rates for plug-in estimators of density level sets
In the context of density level set estimation, we study the convergence of general plug-in methods under two main assumptions on the density for a given level λ. More precisely, it is assumed that the density (i) is smooth in a neighborhood of λ and (ii) has γ -exponent at level λ. Condition (i) ensures that the density can be estimated at a standard nonparametric rate and condition (ii) is si...
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In the context of density level set estimation, we study the convergence of general plug-in methods under two main assumptions on the density for a given level λ. More precisely, it is assumed that the density (i) is smooth in a neighborhood of λ and (ii) has γ-exponent at level λ. Condition (i) ensures that the density can be estimated at a standard nonparametric rate and condition (ii) is sim...
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In bivariate density representation there is an extensive literature on level set estimation when the level is fixed, but this is not so much the case when choosing which level is (or which levels are) of most interest. This is an important practical question which depends on the kind of problem one has to deal with as well as the kind of feature one wishes to highlight in the density, the answ...
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We deal with the problem of representing a bivariate density function by level sets. The choice of which levels are used in this representation are commonly arbitrary (most usual choices being those with probability contents .25, .5 and .75). Choosing which level is (or which levels are) of most interest is an important practical question which depends on the kind of problem one has to deal wit...
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2009
ISSN: 1350-7265
DOI: 10.3150/09-bej184