On multivariate order statistics. Application to ranked set sampling

Authors:
Barry C. Arnold;Enrique Castillo;José María Sarabia
Affiliations:
Department of Statistics, University of California, Riverside, USA;Department of Applied Mathematics, University of Cantabria, Spain;Department of Economics, University of Cantabria, Spain
Venue:
Computational Statistics & Data Analysis
Year:
2009

Citing 5
Cited 0

A Matrix Approach to Finding a Set of Generators and Finding the Polar(Dual) of a Class of Polyhedral Cones

SIAM Journal on Matrix Analysis and Applications
An Orthogonally Based Pivoting Transformation of Matrices and Some Applications

SIAM Journal on Matrix Analysis and Applications
Progressive Type II censored order statistics for multivariate observations

Journal of Multivariate Analysis
Semi-parametric nonlinear regression and transformation using functional networks

Computational Statistics & Data Analysis
How to compare small multivariate samples using nonparametric tests

Computational Statistics & Data Analysis

Quantified Score

Hi-index	0.03

Visualization

Abstract

Two new concepts of order statistics for multivariate samples are introduced. In one of the versions it turns out that not every multivariate order statistic is present in every sample. These order statistics have application in multivariate ranked set sampling and can be used to generate broad classes of multivariate densities in the sense of Jones. In this case the likelihood for the sample values and their corresponding ranks can be calculated based on the conditional density of a multivariate order statistics given its sample value, and such that its integral gives the probability for the multivariate order statistics under discussion to be observed. An alternative version of multivariate order statistics is also introduced, for which multivariate order statistics are always well defined and expressions for their marginal densities are derived. Since these multivariate order statistics are tailor made for multivariate ranked set sampling, their densities allow for parameter inference based on ranked set sampling. Some simulations show that both multivariate order statistics densities can be used with advantage with respect to simple random sampling.