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

Abstract

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.