A Simple Nonparametric Test of Complete Independence

  • Published : 1998.08.01


A simple nonparametric test of complete or total independence is suggested for continuous multivariate distributions. This procedure first discretizes the original variables based on their order statistics, and then tests the hypothesis of complete independence for the resulting contingency table. Under the hypothesis of independence, the chi-squared test statistic has an asymptotic chi-squared distribution. We present a simulation study to illustrate the accuracy in finite samples of the limiting distribution of the test statistic. We compare our method to another nonparametric test of complete independence via a simulation study. Finally, we apply our method to the residuals from a real data set.



  1. Applied Statistics v.39 A Look at Some data on the Old Faithful Geyser Azzalini, A.;Bowman, A.W.
  2. Annals of Mathematical Statistics v.32 Distribution Free Tests of Independence Based on the Sample Distribution Function Blum, J.R.;Kieffer, J.;Rosenblatt, M.
  3. Journal of Multivariate Analysis v.16 Testing for Independence by the Empirical Characteristics Function Csorgo, S.
  4. Journal of the Korean Statistical Society v.27 The Chi-Squared Test of Independence for a Multi-way Contingency Table with All Margins Fixed Park, C.
  5. Sankyha Series A v.32 On a Class of Rank Order Tests for Independence in Multivariate Distributions Puri, M.L.;Sen, P.K.;Gokhale, D.V.
  6. Journal of Multivariate Analysis v.7 Multivariate Nonparametric Tests for Independence Sinha, B.K.;Wieand, H.S.
  7. Annals of Statistics v.12 Asymptotic Normality of a Class of Nonlinear Rank Tests for Independence Shirahata, S.;Wakimoto, K.