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The asymptotic behavior of global errors of functional estimates plays a key role in hypothesis testing and confidence interval building. Whereas for pointwise errors asymptotic normality often easily follows from standard Central Limit Theorems, global errors asymptotics involve some additional techniques such as strong approximation, martingale theory and Poissonization. We review these techniques in the framework of density estimation from independent identically distributed random variables,...
The index of regularity of a measure was introduced by Beirlant, Berlinet and Biau [1] to solve practical problems in nearest neighbour density estimation such as removing bias or selecting the number of neighbours. These authors proved the weak consistency of an estimator based on the nearest neighbour density estimator. In this paper, we study an empirical version of the regularity index and give sufficient conditions for its weak and strong convergence without assuming absolute continuity or...
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