Distribution Theory of Order Statistics of Concomitants Subsets and Applications

• Activity Number: 108
• Type: Contributed
• Date/Time: Monday, July 30, 2007 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Ke Wang*+ and Haikady Nagaraja
• Companies: The Ohio State University and The Ohio State University
• Keywords: order statistics ; concomitants of order statistics ; conditional distribution ; limiting distribution

Abstract

Let (Xi, Yi), i = 1, ..., n be a random sample of size n from an absolutely continuous bivariate distribution F(x, y). We study the finite-sample and asymptotic joint distribution of (V(s:m),W(t:n-m)), where V(s:m) is the s-th order statistic of the concomitants subset {Y[i:n], i=n-m+1,...,n}, and W(t:n-m) is the t-th order statistic of the concomitants subset {Y[j:n], j =1, ..., n-m}. The results are applied to study the probability that at least s of the Y concomitant values, {Y[n-m+1:n], Y[n-m+2:n], ..., Y[n:n]}, are among the top k values of the entire Y -sample. Such events are of interest in selection procedures as described in Yeo and David (1984). We also apply the results to study the power of the two-stage designs for gene-disease association studies as discussed in Satagopan et al. (2002) and Satagopan et al. (2004).