ABSTRACT
This chapter focuses on likelihood ratio statistics and other invariants derived from the likelihood function. Tensor methods are particularly appropriate and powerful because of the requirement that any inferential statement should be materially unaffected by the parameterization chosen. The parameterization is simply a convenient but arbitrary way of specifying the various probability models under consideration. An inferential statement identifies a subset of these distributions and that subset should, in principle at least, be unaffected by the particular parameterization chosen. Particular emphasis is placed on invariants, which may be used to make inferential statements independent of the coordinate system. The most important invariant is the log likelihood function itself. Other invariants are connected with the likelihood ratio statistic and its distribution.
