  The infinite-dimensional information operator for the nuisance parameter
plays a key role in semiparametric inference, as it is closely related to the
regular estimability of the target parameter. Calculation of information
operators has traditionally proceeded in a case-by-case manner and has easily
entailed lengthy derivations with complicated arguments. We develop a unified
framework for this task by exploiting commonality in the form of semiparametric
likelihoods. The general formula allows one to derive information operators
with simple calculus and, if necessary at all, a minimal amount of
probabilistic evaluations. This streamlined approach shows its efficiency and
versatility in application to a number of popular models in survival analysis,
inverse problems, and missing data.
