Efficient Moments-based Permutation Tests

Abstract

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.

Figure 1

Order of all permutation equivalent subsets when d = 2 and r = 2.

Figure 2

Greedy Search Algorithm for computing

Figure 3

(a) and (b): Comparison of techniques in raw p-value measurement at α = 0.05 (without correction), through real permutation ((a); number of permutations = 10,000) and using the present moments-based permutation (b). (c) p-map after BH’s FDR correction of (b). (e) Facial differences between Asian male and white male. Locations in red on the 3D surface denote significant face shape differences (significance level α = 0.01 with false discovery rate control).