Multivariate records based on dominance

Details Multivariate records based on dominance Multivariate records based on dominance

2010-03-30

arxiv.org/abs/1003.6119v1

Mathematics

Statistics Theory

Scientific paper

We consider three types of multivariate records in this paper and derive the mean and the variance of their numbers for independent and uniform random samples from two prototype regions: hypercubes $[0,1]^d$ and $d$-dimensional simplex. Central limit theorems with convergence rates are established when the variance tends to infinity. Effective numerical procedures are also provided for computing the variance constants to high degree of precision.

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