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Let Xn, n ≥ 1, be a sequence of independent and identically distributed random variables and Xn,1≤ Xn,2≤...≤ Xn,ndenote the order statistics of X1,…, Xn. For any sequence of integers {kn} with 1 ≤ kn≤ n and limn→∞min {kn, n − kn+ 1} = ∞, if there exist constants an> 0, bn∈ R and some non-degenerate distribution function G such that (Xn,kn− bn)/ anconverges in distribution to G, then with probability...
This paper deals with nonparametric estimation of the boundary curve of the support of a bivariate density function. This estimation problem arises in various contexts, such as for example scatterpoint image analysis and frontier estimation in econometrics. The setup in this paper is a general one, allowing the bivariate density function to be infinite, bounded away from zero or zero at the boundary...
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