Many multivariate records

Charles M. Goldie and Sidney I. Resnick

Stochastic Processes and their Applications, 1995, vol. 59, issue 2, 185-216

Abstract: (Xn)n=1,2,... is a sequence of independent, identically distributed random vectors in 2. Say Xn is a record if there is a record simultaneously in both coordinates at index n. The total number of records of a sequence is frequently finite so we consider the behaviour of the records in a fixed rectangle A conditional on there being a large number of records NA in the rectangle. We join the records up to form a random parametrized curve, and prove that, under suitable conditions, as the number of records in the rectangle goes to infinity the random curves converge conditionally in probability to a non-random limit parametrized curve, which we characterize. We also prove a large-deviation result for the random curves.

Keywords: Extreme; values; Hazard; measure; Large; deviations; Limiting; curve; Multivariate; record; values; Order; statistics (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (6)

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