Tests of statistical hypotheses concerning several parameters when the number of observations is large

Table of contents 1. Introduction.426 2. Assumptions on the density function/(x, 6).428 3. The joint limit distribution of 0".429 4. Reduction of the general problem to the case of a multivariate normal distribution. .433 5. Tests of simple hypotheses which have uniformly best average power over a family of surfaces.445 6. Tests of simple hypotheses which have best constant power on a family of surfaces. . .450 7. Most stringent tests of simple hypotheses.451 8. Definitions of "best" tests of composite hypotheses.453 9. Tests of linear composite hypotheses which have uniformly best average power over a family of surfaces.455 10.Tests of linear composite hypotheses which have best constant power on a family of surfaces.461 11.Most stringent tests of linear composite hypotheses.461 12.The general composite hypothesis.463 13.Optimum properties of the likelihood ratio test.470 14.Large sample distribution of the likelihood ratio.478 15.