Statistical Problems With Nuisance Parameters

Introduction The multiple Laplace transformation, functions of several complex variables, and analytic sheaves Sufficient statistics and exponential families Nuisance parameters. Tests with invariant power functions Similar tests and statistics Cotest ideals for exponential families Wijsman's $D$-method Unbiased estimates Analytical methods of studying unrandomized tests. Application to the Behrens-Fisher problem Randomized homogeneous tests in the Behrens-Fisher problem. Characterization of tests of the Bartlett-Scheffe type An unrandomized homogeneous similar test in the Behrens-Fisher problem The problem of many small samples Appendix Supplement. New results in the theory of estimation and testing hypotheses for problems with nuisance parameters Bibliography