Efficient Calculation of the Permutation Distribution of Trimmed Means

Abstract The permutation distribution of the trimmed mean in matched-pairs designs is studied. This statistic is important since it is robust to both outliers and distributional assumptions. A polynomial-time algorithm for this inherently exponential-time problem is presented. The characteristic function of the distribution provides both the basis for the algorithm and a vehicle for calculating the asymptotic permutation distribution.

[1]  Bert F. Green,et al.  A Practical Interactive Program for Randomization Tests of Location , 1977 .

[2]  Jackson B. Lackey,et al.  Errata: Handbook of mathematical functions with formulas, graphs, and mathematical tables (Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1964) by Milton Abramowitz and Irene A. Stegun , 1977 .

[3]  Joseph L. Gastwirth,et al.  Small Sample Behavior of Some Robust Linear Estimators of Location , 1970 .

[4]  Herman Chernoff,et al.  ASYMPTOTIC NORMALITY AND EFFICIENCY OF CERTAIN NONPARAMETRIC TEST STATISTICS , 1958 .

[5]  T. E. Doerfler,et al.  The behaviour of some significance tests under experimental randomization , 1969 .

[6]  A. Hope.  A Simplified Monte Carlo Significance Test Procedure , 1968 .

[7]  William J. Welch,et al.  Robust Permutation Tests for Matched-Pairs Designs , 1988 .

[8]  R. D. John,et al.  Significance levels and confidence intervals for permutation tests , 1983 .

[9]  William J. Welch,et al.  Rerandomizing the median in matched-pairs designs , 1987 .

[10]  W. Hoeffding.  The Large-Sample Power of Tests Based on Permutations of Observations , 1952 .

[11]  Louis J. Battan.  Silver-Iodide Seeding and Rainfall from Convective Clouds , 1966 .

[12]  D. Lambert.  Robust Two-Sample Permutation Tests , 1985 .

[13]  Kenneth J. Berry,et al.  Computation of exact and approximate probability values for a matched pairs permutation test , 1985 .

[14]  M. Dwass.  Modified Randomization Tests for Nonparametric Hypotheses , 1957 .

[15]  John W. Tukey,et al.  Approximate behavior of the distribution of Winsorized t (Trimming/Winsorization 2) , 1968 .

[16]  W. J. Hall,et al.  Rerandomization Inference on Regression and Shift Effects: Computationally Feasible Methods , 1983 .

[17]  M. Pagano,et al.  On Obtaining Permutation Distributions in Polynomial Time , 1983 .

[18]  E. Pitman.  Significance Tests Which May be Applied to Samples from Any Populations , 1937 .

[19]  Jeyaraj Vadiveloo.  On the theory of modified randomization tests for nonparametric hypotheses , 1983 .

[20]  P. Bickel.  On Some Robust Estimates of Location , 1965 .

[21]  Charles Stein,et al.  On the Theory of Some Non-Parametric Hypotheses , 1949 .

[22]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[23]  B. L. Welch.  ON THE z-TEST IN RANDOMIZED BLOCKS AND LATIN SQUARES , 1937 .

[24]  E. Brigham,et al.  The fast Fourier transform , 2016, IEEE Spectrum.

[25]  S. Stigler.  The Asymptotic Distribution of the Trimmed Mean , 1973 .

[26]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[27]  Louis A. Jaeckel.  Robust Estimates of Location: Symmetry and Asymmetric Contamination , 1971 .

[28]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

[29]  S. L. Andersen,et al.  Permutation Theory in the Derivation of Robust Criteria and the Study of Departures from Assumption , 1955 .

[30]  Universal asymptotic normality for conditionally trimmed sums , 1988 .

[31]  J. A. Hartigan,et al.  Using Subsample Values as Typical Values , 1969 .

[32]  David Tritchler,et al.  On Inverting Permutation Tests , 1984 .

[33]  J. M. Nelsen,et al.  Clinical and psychological effects of marihuana in man. , 1968, Science.

[34]  R. A. Fisher,et al.  Design of Experiments , 1936 .

[35]  Distribution-free confidence intervals , 1978 .

[36]  D. Mason,et al.  The Asymptotic Distribution of Trimmed Sums , 1988 .

[37]  E. O. Brigham,et al.  The Fast Fourier Transform , 1967, IEEE Transactions on Systems, Man, and Cybernetics.

[38]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[39]  P. Bickel,et al.  Mathematical Statistics: Basic Ideas and Selected Topics , 1977 .

[40]  M. M. Siddiqui,et al.  Robust Estimation of Location , 1967 .

[41]  W. R. van Zwet,et al.  Asymptotic Expansions for the Power of Distributionfree Tests in the Two-Sample Problem , 1976 .