Computational Asymptotics

This paper focuses on both numerical and symbolic methods that may prove to be useful for the purposes of data analysis, but have, so far, not been implemented for routine use in most of the popular statistical packages. Emphasizing likelihood methods I hope to demonstrate that (i)there are situations, where standard numerical algorithms may easily be adapted to yield results more accurately related to respective likelihood quantities than those obtained by quadratic, ‘Wald-type’ approximations;(ii)there are instances, where relying on numerical algorithms may yield results highly sensitive on some quantities that may not be computed to adequate precision; and(iii)symbolic computations may be successfully employed to obtain numerically accurate and mathematically correct results, even if derivations envolved are tedious and too messy to be done by hand.