A Simple Method for Testing Independence of High-Dimensional Random Vectors

Authors

  • Gintautas Jakimauskas Institute of Mathematics and Informatics, Vilnius
  • Marijus Radavičius Institute of Mathematics and Informatics, Vilnius
  • Jurgis Sušinskas Institute of Mathematics and Informatics, Vilnius

DOI:

https://doi.org/10.17713/ajs.v37i1.291

Abstract

A simple, data-driven and computationally efficient procedure for testing independence of high-dimensional random vectors is proposed. The procedure is based on interpretation of testing goodness-of-fit as the classification problem, a special sequential partition procedure, elements of sequential testing, resampling and randomization. Monte Carlo simulations are carried out to assess the performance of the procedure.

References

Baringhaus, L., and Henze, N. (1988). A consistent test for multivariate normality based on the empirical characteristic function. Metrika, 35, 339-348.

Blum, J. R., Kiefer, J., and Rozenblatt, M. (1961). Distribution free tests for independence based on the sample distribution function. Annals of Mathematical Statistics, 35, 138-149.

Bousquet, O., Boucheron, S., and Lugosi, G. (2004). Introduction to statistical Learning Theory. In O. Bousquet, U. von Luxburg, and G. Rätsch (Eds.), Advanced Lectures

on Machine Learning (p. 169-207). New York, Berlin: Springer.

Bowman, A. W., and Foster, P. J. (1993). Adaptive smoothing and density based tests of multivariate normality. Journal of the American Statistical Association, 88, 529-537.

Genest, C., and Remillard, B. (2004). Tests of independence and randomness based on the empirical copula process. Test, 13, 335-370.

Hastie, T., Tibshirani, R., and Friedman, J. H. (2001). The elements of Statistical Learning. New York, Berlin: Springer.

Huang, L.-S. (1997). Testing goodness-of-fit based on a roughness measure. Journal of the American Statistical Association, 92, 1399-1402.

Hyvärinen, A., Karhunen, J., and Oja, E. (2001). Independent Component Analysis. New York: John Wiley and Sons.

Polonik, W. (1999). Concentration and goodness-of-fit in higher dimensions: (asymptotically) distribrution free methods. Annals of Statistics, 27, 1210-1229.

Szekely, G. J., and Rizzo, M. L. (2005). A new test for multivariate normality. Journal of Multivariate Analysis, 93, 58-80.

Szekely, G. J., and Rizzo, M. L. (2006). Testing for equal distributions in high dimension.

Vapnik, V. N. (1998). Statistical Learning Theory. New York: John Wiley and Sons.

Vapnik, V. N., and Chervonenkis, A. (1981). Necessary and sufficient conditions for the uniform convergence of means to their expectations. Theory Probabability and its

Applications, 26, 821-832.

Verdinelli, I., and Wasserman, L. (1998). Bayesian goodness-of-fit testing using infinitedimensional

exponential families. Annals of Statistics, 26, 1215-1241.

Zhu, L., Fang, K. T., and Bhatti, M. I. (1997). On estimated projection pursuit-type Cramér-von Mises statistics. Journal of Multivariate Analysis, 63, 1-14.

Zhu, L.-X., and Neuhaus, G. (2000). Nonparametric Monte Carlo tests for multivariate distributions. Biometrika, 87, 919-928.

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Published

2016-04-03

How to Cite

Jakimauskas, G., Radavičius, M., & Sušinskas, J. (2016). A Simple Method for Testing Independence of High-Dimensional Random Vectors. Austrian Journal of Statistics, 37(1), 101–108. https://doi.org/10.17713/ajs.v37i1.291

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