Statistical tests based on empirical processes and related questions

We consider goodness-of-fit tests for hypotheses about the forms of distributions and their membership in prescribed families of distributions. We first describe the classical tests based on empirical processes such as the omega-square tests of Cramér–von Mises–Smirnov and the Kolmogorov–Smirnov tests. We also consider Shapiro–Wilk tests. We devote a considerable amount of attention to testing the hypothesis that a random variable or vector is normal. We describe tests based on transformations of the empirical process, minimal distance tests and estimates, tests for symmetry, uniformity, and independence, and tests based on spacings. At the end we study methods of computing and the distribution functions of quadratic forms of normal random variables connected with tests of omega-square type. Bibliography: 372 titles.