ABSTRACT
This chapter explains that how index notation simplifies many statistical calculations, particularly those involving moments or cumulants of non-linear functions. Other applications where index notation greatly simplifies matters include k-statistics, Edgeworth and conditional Edgeworth approximations, calculations involving conditional cumulants, moments of maximum likelihood estimators, likelihood ratio statistics and the construction of ancillary statistics. Index notation is a convention for the manipulation of multi-dimensional arrays. The elements of these arrays are called components if they are functions of selected components of the vector of interest. An invariant is a function whose value is unaffected by transformations within a specified class or group.
