Multivariate records based on dominance. (English) Zbl 1225.60043

Hwang, Hsien-Kuei; Tsai, Tsung-Hsi

Electron. J. Probab. 15, Paper No. 60, 1863-1892 (2010).

Summary: 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: the hypercube \([0,1]^d\) and the \(d\)-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 a high degree of precision.

MSC:

60F05	Central limit and other weak theorems
60C05	Combinatorial probability
60G70	Extreme value theory; extremal stochastic processes

Keywords:

multivariate records; Pareto optimality; central limit theorems; Berry-Esseen bound; partial orders; dominance