ABSTRACT
It is, therefore, essential to have widely applicable procedures that in some sense provide good approximate solutions when “exact” solutions are not available. This we now discuss, the central idea being that when the number n of observations is large and errors of estimation correspondingly small, simplifications become available that are not available in general. The rigorous mathematical develop ment involves limiting distributional results holding as n -* and is closely associated with the classical limit theorems of probability theory; full discussion involves careful attention to regularity con ditions and this we do not attempt. Practical application, on the other hand, involves the use of these limiting results as an approxi mation for some finite n. The numerical adequacy of such an approximation always needs consideration; in some cases, we shall be able to extend the discussion to investigate higher-order approxi mations.
