Distribution-Free Statistical MethodsThe preparation of several short courses on distribution-free statisti cal methods for students at third and fourth year level in Australian universities led to the writing ofthis book. My criteria for the courses were, firstly, that the subject should have a clearly recognizable underlying common thread rather than appear to be a collection of isolated techniques. Secondly, some discussion of efficiency seemed essential, at a level where the students could appreciate the reasons for the types of calculations that are performed, and be able actually to do some of them. Thirdly, it seemed desirable to emphasize point and interval estimation rather more strongly than is the case in many of the fairly elementary books in this field. Randomization, or permutation, is the fundamental idea that connects almost all of the methods discussed in this book. Application of randomization techniques to original observations, or simple transformations of the observations, leads generally to conditionally distribution-free inference. Certain transformations, notably 'sign' and 'rank' transformations may lead to unconditionally distribution-free inference. An attendant advantage is that useful tabulations of null distributions of test statistics can be produced. In my experience students find the notion of asymptotic relative efficiency of testing difficult. Therefore it seemed worthwhile to give a rather informal introduction to the relevant ideas and to concentrate on the Pitman 'efficacy' as a measure of efficiency. |
Contents
Miscellaneous onesample problems | 61 |
4 | 67 |
Twosample problems | 83 |
Copyright | |
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A₁ A₂ applied approximately normal asymptotic b₁ B₂ bivariate bution calculations Chapter conditional distribution conditional null distribution confidence interval confidence limits covariance matrix data of Example defined denote density distri distribution function distribution of Q distribution-free methods efficacy efficiency estimate of ẞ estimating equation exact confidence exact distribution exact joint formula given giving graph H₁ Hypothesis testing identical independent inference about ẞ interquartile range invariant with respect joint confidence region joint distribution large-sample linear location parameter M-estimates M₁ mean statistic normal approximation normal distribution null hypothesis observed value obtained pairwise slopes permutation point estimate population possible problem R₁ R₂ random variables rank statistics replaced S₁ S₂ sample median Section sign statistic ẞ₁ ẞ₂ ẞx Suppose t₁ t₂ tabulated test statistic theorem transformations two-sample W₁ W₂ Wilcoxon x₁ Y-sample Y₁ σ²