Efficient Moments-based Permutation Tests

In this paper, we develop an efficient moments-based permutation test approach to improve the test's computational efficiency by approximating the permutation distribution of the test statistic with Pearson distribution series. This approach involves the calculation of the first four moments of the permutation distribution. We propose a novel recursive method to derive these moments theoretically and analytically without any permutation. Experimental results using different test statistics are demonstrated using simulated data and real data. The proposed strategy takes advantage of nonparametric permutation tests and parametric Pearson distribution approximation to achieve both accuracy and efficiency.

[1]  Martin Styner,et al.  ROI constrained statistical surface morphometry , 2007, 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[2]  E. Ziegel.  Permutation, Parametric, and Bootstrap Tests of Hypotheses (3rd ed.) , 2005 .

[3]  P. Good.  Permutation, Parametric, and Bootstrap Tests of Hypotheses (Springer Series in Statistics) , 1994 .

[4]  N. Cox.  Statistical Models in Engineering , 1970 .

[5]  Chunxiao Zhou,et al.  HYBRID PERMUTATION TEST WITH APPLICATION TO SURFACE SHAPE ANALYSIS , 2008 .

[6]  M. Goresky,et al.  An Introduction to Abstract Algebra , 2005 .

[7]  P. Good.  Permutation, Parametric, and Bootstrap Tests of Hypotheses , 2005 .

[8]  Ing Rj Ser.  Approximation Theorems of Mathematical Statistics , 1980 .

[9]  Shin Ta Liu,et al.  Permutation Methods: A Distance Function Approach , 2002, Technometrics.

[10]  Yuxiao Hu,et al.  3D face analysis for distinct features using statistical randomization , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[11]  Thomas E. Nichols,et al.  Nonparametric permutation tests for functional neuroimaging: A primer with examples , 2002, Human brain mapping.

[12]  L. Hubert.  Assignment methods in combinatorial data analysis , 1986 .

[13]  Eugene S. Edgington,et al.  Randomization Tests , 2011, International Encyclopedia of Statistical Science.

[14]  Lawrence J Hubert,et al.  Assignment methods incombinatorial data analysis , 1986 .

[15]  Martin Styner,et al.  Statistical surface-based morphometry using a nonparametric approach , 2004, 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821).