Non-parametric Statistical Methods

Basic statistics and econometrics courses stress methods based on assuming that the data or error term in regression models follow the normal distribution. Indeed, the efficiency of least squares estimates relies on the assumption of normality. In order to lessen the dependence of statistical inference on that assumption statisticians developed methods based on rank tests whose sampling distribution, under the null hypothesis, do not depend on the form of the underlying density function.

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

[2]  H. B. Mann,et al.  On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other , 1947 .

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

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

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

[6]  J. L. Hodges,et al.  Estimates of Location Based on Rank Tests , 1963 .

[7]  J. Gastwirth.  ON ROBUST PROCEDURES , 1966 .

[8]  A. Birnbaum,et al.  Efficiency Robust Two-Sample Rank Tests , 1967 .

[9]  P. Sen,et al.  Theory of rank tests , 1969 .

[10]  Herman Rubin,et al.  The effect of autoregressive dependence on a nonparametric test (Corresp.) , 1967, IEEE Trans. Inf. Theory.

[11]  P. Sen.  Estimates of the Regression Coefficient Based on Kendall's Tau , 1968 .

[12]  Jana Jurečková,et al.  Asymptotic Linearity of a Rank Statistic in Regression Parameter , 1969 .

[13]  J. Oosterhoff.  Combination of one-sided statistical tests , 1969 .

[14]  J. Jurecková,et al.  Nonparametric Estimate of Regression Coefficients , 1971 .

[15]  Herman Rubin,et al.  Effect of Dependence on the Level of Some One-Sample Tests , 1971 .

[16]  P. J. Huber.  The 1972 Wald Lecture Robust Statistics: A Review , 1972 .

[17]  D. Bauer.  Constructing Confidence Sets Using Rank Statistics , 1972 .

[18]  P. Bickel,et al.  On Some Analogues to Linear Combinations of Order Statistics in the Linear Model , 1973 .

[19]  Douglas A. Wolfe,et al.  Nonparametric Statistical Methods , 1973 .

[20]  R. Hogg.  Adaptive Robust Procedures: A Partial Review and Some Suggestions for Future Applications and Theory , 1974 .

[21]  E. Lehmann,et al.  Nonparametrics: Statistical Methods Based on Ranks , 1976 .

[22]  C. D. Kemp,et al.  Statistical Inference Based on Ranks , 1986 .