ABSTRACT
This chapter focuses on statistical inferences such as hypotheses testing, confidence intervals and predictions. To establish these statistical inferences, knowledge of the sampling distributions of some related statistics is necessary. In practice, statistical properties of the sampling distributions can be easily derived under normality assumptions. The likelihood ratio test is the most commonly used. The likelihood ratio test can be obtained based on the likelihood principle. In practice, since it is interest to construct a simultaneous confidence interval for a finite number of estimable functions, H. Scheffe's method may provide wider intervals than other methods in some cases. One advantage of Scheffe's confidence interval, however, is that it can be applied to all linear models without any limitations on the design matrix. Interval is usually referred to as a Bonferroni interval or Bonferroni t-interval. The maximum modulus t-interval is probably the most commonly used method for constructing a simultaneous confidence interval for multivariate normal means.
