TY - JOUR
T1 - Jackknifing two-sample statistics
AU - Schechtman, Edna
AU - Wang, Suojin
N1 - Funding Information:
We would like to thank the reviewers for their insightful and constructive comments and suggestions that led to significant improvements of the paper. Wang's research was supported in part by grants from the Texas Advanced Research Program, the National Cancer Institute (CA 57030), and by the Texas Center for Environmental and Rural Health via a grant from the National Institute of Environmental Health Sciences. Schechtman's research was partially supported by the BGU Paul Ivanier Center for Robotics Research and Production Management.
PY - 2004/2/1
Y1 - 2004/2/1
N2 - In this paper, a new simple method for jackknifing two-sample statistics is proposed. The method is based on a two-step procedure. In the first step, the point estimator is calculated by leaving one X (or Y) out at a time. At the second step, the point estimator obtained in the first step is further jackknifed, leaving one Y (or X) out at a time, resulting in a simple formula for the proposed point estimator. It is shown that by using the two-step procedure, the bias of the point estimator is reduced in terms of asymptotic order, from O(n-1) up to O(n-2), under certain regularity conditions. This conclusion is also confirmed empirically in terms of finite sample numerical examples via a small-scale simulation study. We also discuss the idea of asymptotic bias to obtain parallel results without imposing some conditions that may be difficult to check or too restrictive in practice.
AB - In this paper, a new simple method for jackknifing two-sample statistics is proposed. The method is based on a two-step procedure. In the first step, the point estimator is calculated by leaving one X (or Y) out at a time. At the second step, the point estimator obtained in the first step is further jackknifed, leaving one Y (or X) out at a time, resulting in a simple formula for the proposed point estimator. It is shown that by using the two-step procedure, the bias of the point estimator is reduced in terms of asymptotic order, from O(n-1) up to O(n-2), under certain regularity conditions. This conclusion is also confirmed empirically in terms of finite sample numerical examples via a small-scale simulation study. We also discuss the idea of asymptotic bias to obtain parallel results without imposing some conditions that may be difficult to check or too restrictive in practice.
KW - Bias reduction
KW - Jackknife
KW - Two-sample statistic
KW - U-statistic
UR - http://www.scopus.com/inward/record.url?scp=0242404302&partnerID=8YFLogxK
U2 - 10.1016/S0378-3758(02)00420-2
DO - 10.1016/S0378-3758(02)00420-2
M3 - Article
AN - SCOPUS:0242404302
SN - 0378-3758
VL - 119
SP - 329
EP - 340
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 2
ER -