Asymptotically Nonparametric Inference: An Alternative Approach to Linear Models

As an alternative to the standard analysis of variance, procedures are developed for linear models with several observations per cell which are asymptotically distribution-free and whose asymptotic efficiency relative to the standard procedures is the same as that of the Wilcoxon test relative to Student’s t-test. Specific procedures discussed are (i) tests of linear hypotheses, (ii) confidence intervals for any contrast, (iii) simultaneous intervals for all contrasts.

[1]  E. L. Lehmann,et al.  Robust Estimation in Analysis of Variance , 1963 .

[2]  J. Durbin.  INCOMPLETE BLOCKS IN RANKING EXPERIMENTS , 1951 .

[3]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[4]  Fred C. Andrews,et al.  Asymptotic Behavior of Some Rank Tests for Analysis of Variance , 1954 .

[5]  J. Klotz.  Small Sample Power and Efficiency for the One Sample Wilcoxon and Normal Scores Tests , 1963 .

[6]  Student,et al.  THE PROBABLE ERROR OF A MEAN , 1908 .

[7]  W. Kruskal.  Historical Notes on the Wilcoxon Unpaired Two-Sample Test , 1957 .

[8]  A. Madansky.  More on Length of Confidence Intervals , 1962 .

[9]  Helmert.  Die Genauigkeit der Formel von Peters zur Berechnung des wahrscheinlichen Beobachtungsfehlers directer Beobachtungen gleicher Genauigkeit , 1876 .

[10]  J. L. Hodges,et al.  The Efficiency of Some Nonparametric Competitors of the t-Test , 1956 .

[11]  J. Pratt.  Length of Confidence Intervals , 1961 .

[12]  M. Friedman.  The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance , 1937 .

[13]  J. Wolfowitz.  Minimax Estimates of the Mean of a Normal Distribution with Known Variance , 1950 .

[14]  G. W. Brown,et al.  On Median Tests for Linear Hypotheses , 1951 .

[15]  E. S. Pearson,et al.  On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .

[16]  P. vanElteren,et al.  A generalization of the method of M rankings : (Proceedings KNAW series A, 56(1953), nr 4, Indagationes mathematicae, 15(1953), p 358-369) , 1953 .

[17]  John W. Pratt,et al.  Shorter Confidence Intervals for the Mean of a Normal Distribution with Known Variance , 1963 .

[18]  W. Kruskal,et al.  Use of Ranks in One-Criterion Variance Analysis , 1952 .

[19]  H. Scheffé.  A METHOD FOR JUDGING ALL CONTRASTS IN THE ANALYSIS OF VARIANCE , 1953 .

[20]  J. Wolfowitz,et al.  Introduction to the Theory of Statistics. , 1951 .

[21]  W. R. Buckland,et al.  Statistical Theory and Methodology in Science and Engineering. , 1960 .

[22]  E. S. Pearson,et al.  On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .

[23]  J. L. Hodges,et al.  Rank Methods for Combination of Independent Experiments in Analysis of Variance , 1962 .