On conditional distributions of nearest neighbors

E. Kaufmann and R. -D. Reiss

Journal of Multivariate Analysis, 1992, vol. 42, issue 1, 67-76

Abstract: Let X1, ..., Xn be i.i.d. S-valued random variables and let g be a real-valued function on S. We give an explicit representation of the conditional distribution of the empirical point process based on X1, ..., Xn given the (k + 1)th smallest order statistic of the r.v.'s g(X1), ..., g(Xn). The extension to conditioning on several of the order statistics of g(X1), ..., g(Xn) is indicated. The result for point processes enables us to deduce the conditional distribution of the k smallest g-order statistics taken in the order of their magnitude as well as in the order of their outcome. The latter r.v.'s are conditionally independent.

Keywords: conditional; distribution; nearest; neighbor; empirical; point; processes; g-order; statistics (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (7)

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