ABSTRACT
This chapter shows how cumulant tensors transform under non-linear or non-affine transformation of X. It describes the algorithm that relies heavily on the use of index notation and is easy to implement with the assistance of suitable tables. The maximum likelihood estimator and the maximized likelihood ratio statistic can be expressed as functions of the log likelihood derivatives. In general, it is a good deal more convenient to work with polynomial functions rather than, say, exponential or logarithmic functions of X. The first step in most calculations is therefore to expand the function of interest as a polynomial in X and to truncate at an appropriate point. Just as moments can be expressed as combinations of ordinary cumulants according to, so too generalized cumulants can be expressed in a similar way.
