Asymptotic approximations to the distribution of Kendall's sample
This paper provides a saddlepoint approximation to the distribution of the sample version of Kendall's , which is a measure of association between two samples. The saddlepoint approximation is compared with the Edgeworth and the normal approximations, and with the bootstrap resampling distribution. A numerical study shows that with small sample sizes the saddlepoint approximation outperforms both the normal and the Edgeworth approximations. This paper gives also an analytical comparison between approximated and exact cumulants of the sample Kendall's when the two samples are independent.
normal approximation bootstrap resampling cumulant approximation density estimation edgeworth expansion general saddlepoint approximation u-statistic