Efficient Calculation of Jackknife Confidence Intervals for Rank Statistics

• Main Author: Roger Newson
• Format: Article
• Language: English
• Published: Foundation for Open Access Statistics 2005-12-01
• Series: Journal of Statistical Software
• Subjects: balanced binary search tree; jackknife; confidence interval; rank statistics; Kendall’s tau; Somers’ D; Harrell’s c; ROC area; Gini coefficient; sign test; rank-sum test
• Online Access: http://www.jstatsoft.org/v15/i01/paper

An algorithm is presented for calculating concordance-discordance totals in a time of order N log N , where N is the number of observations, using a balanced binary search tree. These totals can be used to calculate jackknife estimates and confidence limits in the same time order for a very wide range of rank statistics, including Kendall’s tau, Somers’ D, Harrell’s c, the area under the receiver operating characteristic (ROC) curve, the Gini coefficient, and the parameters underlying the sign and rank-sum tests. A Stata package is introduced for calculating confidence intervals for these rank statistics using this algorithm, which has been implemented in the Mata compilable matrix programming language supplied with Stata