Maritz J.S. Distribution-Free Statistical Methods

2nd edition. — New York: Chapman and Hall/CRC, 1995. — 268 p.Distribution-free statistical methods enable users to make statistical inferences with minimum assumptions about the population in question. They are widely used, especially in the areas of medical and psychological research.
This new edition is aimed at senior undergraduate and graduate level. It also includes a discussion of new techniques that have arisen as a result of improvements in statistical computing. Interest in estimation techniques has particularly grown, and this section of the book has been expanded accordingly. Finally, Distribution-Free Statistical Methods includes more examples with actual data sets appearing in the text.Basic concepts in distribution-free methodsRandomization and exact tests
Test statistics and estimating equations
Consistency in the one parameter case
Confidence limits
Efficiency considerations in the one parameter case
Estimation
Hypothesis testing
Estimation of standard errors
Multiple samples and parametersPoint estimation
Hypothesis testing
Confidence regions
Normal approximations
The need for normal and related approximations
The central limit theorem
Sampling from finite populations
Linear rank statistics
One-sample location problemsThe mean
The median
Other measures of location
The median
The sign statistic
The null distribution of the sign statistic
Hypothesis testing
Confidence limits for θ
Point estimation of θ
Estimating the standard error of the sample median
Efficiency considerations
Computational notes
Symmetric distributions
The mean statistic
Hypothesis testing
Confidence limits
Normal approximations
Point estimation and efficiency considerations
Computational note
The Wilcoxon signed rank statistic
The null distribution of W
Hypothesis testing
Confidence limits
Point estimation based on W
Efficiency
Estimating the variance of the Hodges-Lehmann estimate
Computational notes
Other rank based transformations
Scores based directly on ranks
The null distribution of wθ
Hypothesis testing
Confidence limits
Point estimation
Efficiency
Optimum rank statistics
Robust transformations
M-estimates
Hypothesis testing and confidence limits
Point estimation and efficiency
M-estimation and scaling
Hypothesis testing
Point estimation and confidence limits
Estimating the variance of an M-estimate
L-estimates
Ties
Asymmetric distributions: M-estimates
Miscellaneous one-sample problemsDispersion: the interquartile range
Symmetric F, known location
General F
The sample distribution function
One-sided confidence bands for F
Estimation of densities
Estimation of F when some observations are censored
The actuarial method of estimating F
The product-limit estimate of F
Paired comparisons
Signed rank tests
Sign tests
Two-sample problems
Types of two-sample problems
The basic randomization argument
Inference about location differenceThe two-sample mean statistic
The two-sample sign statistic
The two-sample rank sum statistic
Two-sample transformed rank statistics
Robust transformations in the two-sample case
Multiplicative models
Proportional hazards (Lehmann alternative)
The Wilcoxon statistic and inference about α
The 'log-rank' test and inference about α
Conditional likelihood and the log-rank test
The log-rank test and censored observations
Dispersion alternatives
A randomized exact test of dispersion
Comparing interquartile ranges
Rank test for dispersion
Straight line regression
The model and some preliminaries
Inference about β only
Inference based on untransformed residuals
Rank transformation of residuals
Sign transformation
Optimal weights for statistics of type T
Theil's statistic, Kendall's rank correlation
Robust transformations
Computational notes
Joint inference about α and β
Median regression
Symmetric untransformed residuals
Symmetric residuals: signed rank method
Symmetric residuals: scores based on ranks
Symmetric residuals: robust transformations
Multiple regression and general linear modelsPlane regression: two independent variables
Inference about slopes: joint conditional distributions
Rank statistics for slopes
Sign statistics for slopes
Joint confidence regions
Point estimation
Consistency and efficiency
Estimating the covariance matrix
Inference about intercepts and slopes
Sign statistics
Symmetric residuals
Signed ranks
Robust transforms
General linear models
Inference about slopes only
Mean statistics
One-way analysis of variance
Randomized blocks: two-way analysis of variance
Exact inference using restricted randomization
Inference about individual regression coefficients
Rank transformations
Grouping and restricted randomization
Bivariate problemsTests of correlation
Conditional permutation tests: the product moment correlation coefficient
Rank transfonnation: Spearman correlation
Sign transformation
Kendall's τ and Theil's statistic
Mean square successive difference test
Contingency tables, correlation ratios
Computational notes
One-sample location
Medians
Hypothesis testing
Confidence regions
Point estimation
Symmetric distributions
Hypothesis testing
Confidence regions
Point estimation
Symmetric distributions: transformation of observations
Symmetric distributions: sign statistics
Symmetric distributions: rank statistics
Hypothesis testing and confidence limits
Point estimation
Two-sampe location problems
Introduction: randomization
Medians and sign tests
Testing a specified (Bx By)
Confidence regions and point estimation
Mean statistics
Hypothesis testing and confidence limits
Point estimation
Alternative calculation of QA
Rank statistics
Confidence regions, point estimation
Other transfomations of (u;, v;)
Three-sample location problems
Miscellaneous complements
Linearization representation
Asymptotic relative efficiency
Estimating equations and the smoothing of statistics
Least squares smoothing
Kernel gradient estimates
Kernel density estimation
Estimating the mean density
Bootstrap estimation of standard errors
Conditional standard errors
Introduction and definitions
Large sample calculations