Statistical Inference: An Integrated Approach

I carefully read the short chapter on goodness-of-Ž t tests (Chap. 6), and it is lacking in several respects, including the coverage of topics and the conclusions presented. For instance, Sherman (1950) provided the exact distribution function—not just the moments—of what has been called here the Kendall–Sherman statistic. There is no need to approximate its distribution by a Pearson type III curve, as is stated at the end of the chapter. (Additional information regarding this issue can be found in Russell and Levitin 1995 and Gatto and Jammalamadaka 1999.) The simulated powers presented in the chapter clearly depend very much on the alternatives used, and to conclude based on the limited simulations that the “Kendall–Sherman goodness-of-Ž t test appears to have distinct advantage over the Kolmogorov goodness-of-Ž t test” is misleading. There is considerable literature on this topic, including asymptotic efŽ ciency comparisons, and it is generally conceded that among tests based on coverages, Greenwood–Moran is better than Kendall–Sherman. As a class, the tests based on coverages are not as good as those based on empirical distribution functions, like the Kolmogorov test. Chapter 6 is, of course, not necessarily representative of the rest of the book, which is well written and thorough. The material in the book is easily accessible to upper-division undergraduates and beginning graduates. Permutation Methods: A Distance Function Approach is a welcome addition to the literature on permutation tests, and the computer package available with it is an added attractive feature.