ABSTRACT
This chapter addresses problems of a more inferential flavour, namely problems concerning point estimation or, better, interval estimation of population cumulants based on observed data. In addition, the variance of such an estimate depends on cumulants up to twice the order of the estimand and these are even more difficult to estimate accurately. The emphasis is on the various symmetric functions, that is, functions of the data that are unaffected by reordering the data values. The chapter is concerned with simple random samples from an infinite population. The emphasis is on the various symmetric functions, functions of the data that are unaffected by reordering the data values. It estimates of cumulants and cumulant products in the presence of identifiable systematic structure, typically in the mean value. The rationale for this requirement is that the joint distribution is unaffected by permuting the observations and therefore any derived statistics should be similarly unaffected.
